Review and Reflect on Physics 2011

What is physics?

Physics, to me, is the study of how energy works. Energy is a force, power, heat, speed of an object, work, wavelength or frequency of something.

What did you think about the class?

The class was fun and wasn't as hard as I thought it would be. We (the students) did a lot of work, not too much, but enough to get through the units. Mr. Blake kept us in check and was really cool, he knew what he was doing and got us to do everything on time or a little bit early so we could just chill.

What did you learn in the class?

I learned to turn off the lights when I don't need to use them cause the electric company charges so much (in cents) per kilowatt-hour. It's not per kilowatt per hour is the amount of energy equivalent to a steady power of 1 kilowatt running for 1 hour. I also learned how to spear fish, cause water makes the image of the fish look closer than it really is so you aim farther. The rest of the stuff I learned was how to find distance, time, initial and final velocities using kinematic equations and also how to calculate mass, force, the normal, weight, wavelength, frequency and other variables with other equations we acquired over time.

What did you like about the class?

I liked how we go to do a lot of group activities, cause if I did it by myself I would have messed up. Plus I like my group a lot, we laughed a lot cause of.... just cause. We worked well in a weird way, even though we sometimes argued (the arguments were not intense, just so you know). I also liked how Mr. Blake made everything fun and had a sense of humor. If he didn't I would have fallen asleep.

What could be modified to improve on the class?

Well, the wording of the questions or problems could have been worded differently because sometimes it was hard to understand what the question was asking us to do. It would take me a little longer to finish tests because I couldn't understand what was going on. Other than that I had no problem with anything else.

Commentary/Feedback?
The class was fun... my group was cool....

Here is the really big roller coaster at Disney's California Adventure Park, as the coaster reaches the top it gets slower then when it drops down the velocity/speed increases a lot. This is what we learned in units 2 and 3.

Unit Ten: Ray Types

 

Today's demonstration of.... light bending...?

There are three different kinds of rays: parallel, focal, and central rays. Parallel rays are parallel to the optic axis and then bend towards the focal point on the image. Focal rays will go through the focal point on the object side and then bend parallel to the optic axis. Central (chief) rays go through the center of the lens and don't bend. Whether these rays converge or not will categorize the type of image that the lens reflects. If the light rays converge then the image is real, if the light rays do not converge then the image is virtual. What side the rays converge also help further categorize the type of image the lens reflects. If the rays converge above the optic axis then the image is upright, if the rays converge below the optic axis then the image is inverted. The distance from the axis will determine whether the image is enlarged or reduced.

Unit Ten: Color Mixing

Here is what we did today, lasers!

What did we learn today? One thing we learned is that you shouldn't look directly into a laser. Real dumb if you did. Another thing we learned was color mixing, not paint mixing cause we learned that in like kindergarten. The type of mixing we talked about was light mixing. The primary colors for lights are red, blue, and green. Red and green equal yellow. Red and blue equal magenta. Green and blue equal cyan. When you add them all together the color you will then get is white. When you add certain colors in different scenarios you can get these results:
Magenta + Yellow = pink, because magenta is made of red and blue and yellow is made of red and green. Red, green and blue equal white but you are also left with the extra red so red plus white equals pink.

Unit Ten: Light

The EM spectrum or electromagnetic spectrum is the range of all possible frequencies of electromagnetic waves (radiation). Electromagnetic waves are radiation consisting of of waves of energy associated with electric and magnetic fields resulting from the acceleration of an electric charge. The spectrum shows the lowest frequencies to the highest frequencies. Radio waves are the lowest type of radiation, it's frequency ranges between 500 - 1000 kHz. Microwaves are greater than radio waves, it's frequency ranges between 10⁹ - 10¹¹ Hz. Infrared is greater than microwaves, it's frequency ranges between 10¹¹ - 10¹⁴ Hz. Visible light (radiation) is visible to the human eye and it's frequency ranges between 4 × 10¹⁴ - 7 × 10¹⁴ Hz, the colors in the visible spectrum consist of (from lowest frequency to highest) red, orange, yellow, green, blue, indigo, and violet. Ultraviolet rays have a frequency between 10¹⁴ - 10¹⁷ Hz, this can cause skin cancer and cataracts. X-rays have a frequency between 10¹⁷ - 10¹⁹ Hz, they can penetrate though objects so they are used to view bones, tumors and ect. Gamma rays have the highest frequencies that are greater than 10¹⁹ Hz.

Here is visible light, yeah I know, it's simple....

Unit Nine: Waves & Sound

Today we went over standing waves, natural frequency, and resonance. A standing wave is a wave that remains in a constant position. Natural frequency is the frequency an object wants to vibrate, it is determined by the object's shape and/or other characteristics. Resonance is the overall adding of wave energies. We also went over sound, sound is a longitudinal wave and it needs a medium. Sound is like any other wave and it's wave speed is measured by it's frequency multiplied by it's wavelength, or v = fλ. The published value of the speed of sound in the air at room temperature is 343 m/s. Right now in our classroom the temperature is 76˚ F. To convert the temperature from Fahrenheit to Celsius you use this formula, [(given Fahrenheit) - 32] × 5/9. So the temperature in the classroom in Celsius is 24.4˚C. The reason why we need to know the temperature is because to calculate speed of sound in the room you use this formula: 331m/s + Tc(0.6).

Today we used these cylinders to measure measure the wavelengths and speeds of different frequency in the room.

Unit Nine: Waves

A wave is a periodic disturbance of the particles of a substance that may be transmitted without net movement of the particles, such as in the passage of surging motion, heat, or sound. The speed at which the wave is moving at is measured by the equation: v = fλ. v is velocity (m/s), f is frequency and λ is wavelength. Frequency is the number of cycles per second which is measured in units of Hertz, Hz. Frequency is also related to period which is the duration of one complete cycle of a wave or oscillation. Wavelength is the difference between two crests or two troughs of a wave. Crests are the the tops of the wave and troughs are the bottom points of the wave. 

Today we used Slinky's to demonstrate constructive and deconstructive amplitudes.

Rocket Building: Parachutes

So today we finished making our parachute. The parachute was 24 inches in diameter and there were eight strings attached to it. We folded it so it could unravel without getting the strings tangled. During our first launch, the parachute didn't deploy. On the second launch, the parachute deployed beautifully but the nose cone fell off too early. After that the parachute didn't deploy until our fifth or sixth launch but it didn't really matter cause it was about one or two feet above the ground. The launches after that were stupidly lame and the nose cone didn't come off or the parachute didn't deploy plus our rocket started to spiral in weird directions. We don't know why the rocket started to move funny but what we do know is, is that our nose cone started to stick to our rocket and caused everything to suck. We learned about how much mass affected our rocket, how much water we needed to get the rocket up high and how much pressure is needed. The mass was not a problem, the fins were not light but they were sturdy. The nose cone had enough mass cause it was an athletic cone and had clay in it to weigh it down. When we added water we made sure that we filled it up to at least half the bottle. We tried to keep the water constant as much as possible. For the pressure, the pump nozzle gave us a hard time cause it kept leaking out the water and made the pressure less on our rocket. Other than that we didn't learn anything else.

When we folded the parachute we had each hole that had string tide to it folded next another one. Each side had four holes. We then had the string folded in the middle and then we wrapped the parachute around the string like a quesadilla. This made the parachute deploy without hassle like in our second launch.

Rocket Building

So today Amber and I started to work on our rocket. Here's the list of materials we used:

1. Two 2-liter bottles
2. An athletic cone
3. Duct tape
4. String
5. Garbage bag
6. Poster board paper
7. Clay/play dough
8. Scissors
9. Hole puncher
10. Water

What we basically did was cut one of the bottles so that only the part in between the top and bottom of the bottle is left. We then taped the cut up bottle to the intact bottle's bottom and used two layers of duct tape just in case. After that we put the athletic cone on the cut up bottle side of the rocket. The cone was too big, so Amber had to cut it because I'm weak. After we cut the cone we taped some string to it and the rocket so when the rocket launches the nose cone (athletic cone) would come off and the parachute would be able to work. With the nose cone now attached I started to cut out three fins for the rocket. We decided to have three because the fins would have added more mass to the bottom of the rocket and the rocket wouldn't stay up in the air for 5 or 10 seconds. We cut out the fins from the poster board paper and to make attaching the fins easier we had an extra centimeter on the two sides that would be taped to the rockets, like this:

http://www.lnhs.org/hayhurst/rockets/

http://www.lnhs.org/hayhurst/rockets/

So after we taped the three fins, Amber constructed our test parachute. She cut the garbage bag and taped eight equally spaced spots on the edges of the garbage bag, she then hole punched each taped spot and tied a string to each hole. We taped the parachute to the rocket and put it in the nose cone. We then launched the rocket and our time was 7.06 seconds. Pretty good since we didn't have a clue on what to do.

Unit Eight: Power

Today in physics we talked about power. Power is the rate at which work is being done. So power = work/interval of time = Joules/seconds = watt. We also worked on how to use the equations from last class which are:

W = Fd

PEg = mgh

PEs = ½kd²

Fs = -kd

KE = ½mv²
∆E = W = f×d = mg×h

W = work

F = force

d = distance

m = mass

g = gravity = 9.8 m/s² ≈ 10m/s²

v = velocity
h = height
∆E = total energy

PEg = Potential Energy (gravitational)
PEs = Potential Energy (of spring)
Fs = Force of spring
KE = kinetic energy

With the given variables you could calculate a machine's (because objects don't move on their own) potential or kinetic energy. Like for example, (just so you know these numbers I am about to use may not logically make sense so just go with it) a machine with a mass of 60 kg walks up one flight of stairs with a distance of 4 m.

1. Calculate the work done by the machine.
2. Find the velocity.

To find #1:
Using the equation we learned from earlier units, F = ma, it should look like this: F = 60kg×9.8m/s². F = 588 N. Now that you know the force, you can use the equation W = F×d, it should look like this: W = 588N×4m. W = 2.352×10³ J.

To find #2:
Using the equations KE = ½mv² and PEg = mgh, input the givens into the equations so it looks like this:

½(60kg)(v)² = 60kg(9.8m/s²)(4m)

Now calculate:

½(60kg)(v)² = 2.352×10³ J

60kg(v)² = 4.704×10³ J

v² = 78.4 N m²/s²

v ≈ 8.9 m/s

Here is the machine/robot going up the flight of stairs.

Unit Eight: Work & Energy

Work = w = any change in energy = ∆E
w = force x distance = N x m
Units = Joules

The Law of Conservation of Energy: energy cannot be created nor destroyed, it only changes form.

Work Energy Thereom  = total initial energy = total energy out

Potential Energy (gravitational) = PEg = Ug = total energy = w = f x d = mg x h.
Potential Energy is the energy possessed by a body by virtue of its position relative to others.

Kinetic Energy = KE = K = ½mv²

 Here is a video of my sister "working". XD

Egg Drop Lab

 

My partner was Amber, it was so awesome. The physics involved: the mass of our capsule and the egg was 1.0956 kg, the velocity was estimated to be 10 m/s, the momentum and change in momentum was estimated to at 11 kg∗m/s. Why our capsule worked: basically our capsule had the biggest mass out of all the other capsules, because of the amount of cushion we used. We used layer after layer of towel and this weird white sticky stuff that people use so their dishes and stuff don't fall down. Plus we put the egg into a sock and then put that sock into another sock. So, we pretty much made up for the fact that our capsule's mass was so huge. All that cushion surrounding the egg kept the egg from cracking, because when the egg's force went downward it hit the many layers of towels and was cushioned and if the egg bounced upward then the other layers of towels cushioned the force. 

What happened during the drop, Amber was on the third floor of the building which is supposedly 10 meters high.... Because of how big the mass of our capsule was air resistance didn't affect it significantly. It pretty much was in free fall and when it reached the ground it made a very ominous, loud sound. The capsule didn't even bounce. But because the intense cushioning our egg was intact and our capsule was still clean.


I would have gotten a smaller box, if I had to do this again because cutting cardboard with broken scissors sucks. Like, I'll admit, I'm weak and if I didn't have Amber I would have been screwed, but those scissors sucked. If I had gotten a smaller box, then our capsule wouldn't have looked so sketch or resemble a bomb.... Though I wouldn't make it significantly smaller because the mass of our original wasn't heavily affected by air resistance.

Unit Seven: Momentum and Impulse

Yesterday we went over momentum, momentum can be calculated with these equations:

p = m(￫v)

1. p = momentum = units: kg∗m/s
2. m = mass = units: kg
3. ￫v = velocity = units: m/s

Impulse is the average force upon the object multiplied by the time the force is acting on the subject. It is also the change in momentum of the object divided by the change in time.

Impulse = ∆p = (¯F)∗∆t = mv - mvo

1. (¯F) = average force = units: Newtons, N or kg∗m/s^2
2. ∆p = change in momentum = units: kg∗m/s
3. ∆t = change in time = units: seconds, s
4. m = mass
5. vo = initial velocity
6. v = final velocity

 Force is the change in momentum divided by the change in time: (¯F) = ∆p÷∆t.

Here is the boxing game on the Wii fit. Yes, I know, this is lame. Anyway when the boxer dude hits that weird robot thing, his punch exerts momentum on the robot.

Unit Seven: Momentum

Momentum or inertia in motion, is what we are learning in unit 7. Momentum is the mass of an object multiplied by the velocity the object is moving at, this is the equation we learned and used today:

∆p = m(￫v)

1. ∆p = total momentum = units: kg x m/s
2. m = mass = units: kg
3. ￫v = velocity (￫ means it's a vector) = units: m/s

Like velocity, there is an initial momentum pin and a final momentum. When an object collides it will start and end with the same momentum, because momentum is conserved. Conserved means to maintain (a quantity such as energy or mass) at a constant overall total, so momentum stays constant.

Reflection of the First Semester....

What you learned?
I learned about kinematics and the equations used to find distance, time, initial velocity and final velocity. This was from units 2 and 3. In class, we continued to use kinematic equations to find diagonal motion and plot variables on t-chart in unit 4. Units 5 and 6 were about forces; balanced and unbalanced. We learned how to calculate the amount of force on an object with the measuring unit called Newtons or N, N = kg(m/s²). 

What was enjoyable about the class?
If I said that I liked doing the conversions and stressing about getting the blog in on time then I'd be a dumby. Not saying it was horrific, it was okay, but I'm not ecstatic about it. I enjoy the people on my table. They're cool. I like how today we did something (slip-n-slide) that was not totally engulfed in physics.

Challenges in physics or otherwise?
The last two units really sucked. Cause it got super confusing sometimes, like when we had to calculate the tension you don't know which mass is the one you should use. Plus the whole thing with direction of the forces and sometimes drawing the free body diagrams were hard to understand and do. Just that I guess.

 

Unit Six: Unbalanced Forces part 2

To depict the forces acting upon an object you would draw out a free body diagram. A free body diagram is a diagram showing all the forces exerted on an object with all its surroundings removed. The diagram consists mostly of a sketch of the object stated and arrows representing the forces exerted upon it. For example:

Here is a yoyo hanging from a string. It is at rest.

Here is the free body diagram of the forces:

The bottom picture is how you would depict forces that are balanced; here is an example of unbalanced:

·            A basketball is moving to the left with friction.

·            The normal force and the weight are balanced but there is no opposite force to balance out the friction.

·            So this is unbalanced.

We also learned how to calculate the acceleration of two objects on a pulley. Here is an example:

The blue box has the same tension and mass as the green box, the normal force and weight of the blue box are balanced but there is negative tension on the blue box as it moves towards the pulley. The green box's positive tension pulling up and the weight are balanced. The mass of the boxes are 12 kg. Now this is how you find the net force and the acceleration of the situation.

 

Let's start with acceleration, you know the mass and the Earth's gravitational pull (10 m/s² ). So now using the equation mBg + t2 - t1 = (mB + mA)a. mBg is the green box's weight, mB is the green box's mass, mA is the blue box's mass, t2 is the green box's tension, t1 is the blue box's tension, and "a" is the system's acceleration. So plugging in the variables, you'll get:

 

12kg(10 m/s²) + t2 - t1 = (12kg +12kg)a

 

Since the tensions are equal they cancel each other out and then you get:

 

120N = (24kg)a

Now to find the acceleration, you divide the mBg over the sum of mB + mA:

120N/24kg = a

a = 5 m/s²

And now, to find the system's net force you'll use the mass (12kg, because both objects are of same mass) and the acceleration you found above (5 m/s²) as your variables with the equation:

Fnet = ma

Fnet = (12 kg)(5 m/s²)

Fnet = 60 N

So that is how you find acceleration and the force net of a system.

Unit Six: Newton's Laws and Unbalanced Forces

So basically, we didn't learn anything new in class but were instructed to do this blog so here it goes…

Unit 6, its about unbalanced forces and Newton's Laws. The opposite of unbalanced forces are balanced forces and balanced forces are, for example:

When a cellphone is placed on a table, and two forces are acting upon said cellphone. One is Earth's gravitational pull and it exerts a downward force. The other is the normal force or the component perpendicular to the surface of the contact, which in this case is the surface of the table, which exerts contact force between the cellphone and the table. The normal pushes upward on the cellphone. These forces are of equal magnitude and are moving in opposite directions, so the forces on the cellphone are balanced.

Now unbalanced forces are, for example:

When the cellphone is given a little push and set into motion from a rest. There are three forces acting upon the moving cellphone. One is Earth's gravitational pull, exerting a downward force on the phone.  The second is the normal force and it exerts an upward pull. The last force is friction, a force that opposes motion or potential motion on an object,  and it is directed opposite the cellphone's motion and will eventually cause the phone to slow down. The gravitational pull and the normal force are of equal magnitude and balance each other out but because there is no force that is of equal magnitude and of opposite direction there is nothing to balance the frictional force. What it comes down to is that the cellphone is not at equilibrium and then accelerates because unbalanced forces cause acceleration.

Here is an example of unbalanced forces, here I have a gift one of my friends got me (yes itʻs a ball, but itʻs the thought that counts), the ball was acted upon by a force that caused it to become unbalanced which led to its slow acceleration.... Well you get it... I hope :P


All of the information I found is from http://www.physicsclassroom.com/class/newtlaws/u2l1d.cfm

Unit Five: Newton's Laws and Equilibrium

In physics, we went over Newton's Law. Last night's post was also about Newton's Laws but were from the Internet. Today, Mr. Blake gave out the terms we needed to know for class for each law.

1.     Newton's First Law

a.     The Law of Inertia

b.     Objects at rest will stay at rest and objects in motion will tend to stay in motion unless acted upon outside unbalanced forces.

2.     Newton's Second Law

a.     The acceleration of an object is directly proportional to the net force on an object and acceleration is inversely proportionate to the object's mass.

                                               i.     a ∝ Fnet

                                              ii.   a ∝ 1/m

                                            iii.     a = Fnet/m

                                            iv.     Fnet = ma

b.     These equations mean that i) the acceleration of an object is directly proportionate to the force net of the same object, ii) the acceleration of an object is inversely proportionate to the mass of the same object, iii) the acceleration of an object equals the force net over the mass of the same object, iv) the force net on an object equals the mass times the acceleration of the same object.

3.     Newton's Third Law

a.     Action – Reaction

b.     For every action/force, there is an equal and opposite force/direction.

Here are some other things that you should know:

1.     Force – a push or pull

2.     Frictional  forces – forces that opposes motion or impending motion

3.     Contact forces – a force that acts at the point of contact of two objects

4.     Distance force – a force at a distance

5.     Balanced forces – uniform motions, or equilibrium that have no acceleration

Me being totally lame and trying to push my huge sofa to represent push and friction

Me being even more lame and trying to pull my other sofa to represent tension.

Unit Five: Newton's Three Laws

Newton's Laws:

Law number one, an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an external force (physicsclassroom.com). It is basically saying that if you are not moving then you don't leave the spot you are situated at. And if you are moving at the same speed and going in the same direction then you stay in a constant motion. So basically it's like standing at the crosswalk, waiting for the pedestrian light to say go. You stay at the curb waiting for the light so you are technically at rest. When the light says go you are moving at a constant speed till you reach the other side which is in the same direction with no change, so you are now in motion.

 

Here is a animation of rest and motion.

Law number two, the acceleration of an object is dependent upon two variables,  the net force acting upon the object and the mass of the object (physicsclassroom.com). Basically the acceleration of an object depends on: the net force which is the overall force or the sum of all forces acting on the object which is directly dependent, and the mass of the object which is inversely dependent. The overall force is like a basketball game, a successful play is dependent on your teammates, the other team and their plays. These together are like the overall force on an object. For mass, I think you guys get that, though mass is not weight it is still a measurement of something. 

Here is a really junk computer drawing of a play that I sort of remember doing when I went to KMS (Kaimuki Middle School), it represents overall force.

Law number three; for every action, there is an equal and opposite attraction (physicsclassroom.com). In translation, this means that forces come in pairs, that the size of the forces on the first object is the same size of the force for the second object, and that the direction of the force on the first object is the opposite direction of the second object. Like how everything comes in pairs, table items come in pairs like salt and pepper, sugar and cream, and ketchup and mustard. The opposite tastes are what make the taste buds neutralize... IDK....

Here is a animation of pairs, remember Mr. Salt and Mr. Pepper? Lol, well, yeah. :D

 

Just an animation I made...nbd...

Unit Four: Diagonals

Diagonals, in physics diagonals are a pain in the butt hole, especially when you try to calculate an object with a diagonal velocity. This is just a fast, to the point post on how to calculate a diagonal velocity's distance or time.

So this is how you start finding the values for your t-chart. You still need to use a t-chart because; a diagonal velocity is basically the vertical over the horizontal velocity. Anyway this is how you find the vertical and horizontal velocities:

1.     Know your givens: in these types of problems you are given the velocity of the diagonal and the angle of the diagonal.

2.     Remember and use SOH CAH TOA:

a.     SOH = sine = opposite/hypotenuse

b.     CAH = cosine = adjacent/hypotenuse

c.      TOA = tangent = opposite/adjacent

d.     The reason for why we need to know SOH CAH TOA is because, the diagonal velocity is like the hypotenuse of a right triangle and the horizontal and vertical velocities are like the adjacent and opposite sides of the triangle from the given angle.

3.     When finding:

a.     Vertical velocity, using the variables given which is the diagonal velocity and the angle, draw out the diagonal direction and triangle shape with the angle of the diagonal. Then, identify which is the opposite and which is the adjacent side of the angle. The opposite side equals the vertical velocity so using SOH CAH TOA you find the vertical velocity with the equation V_oy = (diagonal velocity) sinθ. (θ = the angle given)

b.     Horizontal velocity, it is the same as finding vertical velocity except instead of using sine you will replace it with cosine so the equation will look like this: V_ox = (diagonal velocity) cosθ.

So after you find the vertical and horizontal velocities, the diagonal velocity no longer exists and you use the vertical and horizontal velocities to find the other variables are in your t-chart. You already know the two initial velocities, the accelerations (vertical velocity = -9.8 m/s² acceleration and horizontal velocity = 0 m/s² acceleration), and the final velocity for the horizontal velocity, which is the same as the initial horizontal velocity. So all that is left to find are the distances, times and the final vertical velocity. You find these variables using the kinematic equations. Here is an example:

1.     Given variables: 150 m/s diagonal at 37°.

2.     Find the horizontal and vertical velocity:

a.     V_ox = cosine = (150 m/s)cos37° ≈ 119.8 m/s

b.     V_oy = sine = (150 m/s)sin37° ≈ 119.8 m/s

3.     Make a t-chart with what you already know:

a.     The initial vertical and horizontal velocities

b.     The accelerations for both the x-axis (0 m/s²) and the y-axis (-9.8 m/s²)

c.      The final vertical and horizontal velocities, because the x-axis has an acceleration of 0 m/s² so the final velocity is the same as the initial (119.8 m/s) and for the vertical velocities since it is a vector and is defined by magnitude and direction and since the direction is going downward the final velocity is the negative of the initial which is -119.8 m/s.

4.     Find the missing variables: both distances and the times:

a.     For the times, use the equation V_f = V_o + at.

                                               i.     -119.8 m/s = 119.8 m/s + (-9.8 m/s²)t

                                              ii.     -239.6 m/s =(-9.8 m/s²)t

                                            iii.     t = 24.449s ≈ 24.45s

                                            iv.     because time is a constant both the x and y-axis times are equal

b.     Find the vertical distance, use the equation dy = ½ ay(ty)² + Voy(ty)

                                               i.     dy = ½ (-9.8 m/s²)(24.45s)² + 119.8 m/s(24.45s)

                                              ii.     dy = -2929.23225m + 2929.11

                                            iii.     dy = -0.12225m

c.      Find the horizontal distance, use the equation dx = ½ ax(tx)² + Vox(tx)

                                               i.     dx = ½ (0m/s²)(24.45s)² + 119.8 m/s(24.45s)

                                              ii.     dx = 0 + 119.8 m/s(24.45s)

                                            iii.     dx = 2929.11 m

So that is how you find the variables.

Here is the Disney version of Robin Hood and here he is shooting an arrow at 150 m/s at 37 °.

Unit Four: The T-Chart and Projectiles

So far in unit four we learned about t-charts and how to calculate the speed, time and distance of a projectile. We are still using the same variables from the last two units, which are:

d = distance (meters)

a = acceleration (gravity of Earth = 9.8 m/s² or 10 m/s²)

t = time (seconds)

V_f = final velocity (m/s)

V_o = initial velocity (m/s)

And we are still using the kinematic equations we used in the last two units as well, they are:

d = (average V)t

d = ½ at² + V_ot

V_f = V_o + at

V_f² = V_o² + 2ad

T-charts list x-axis variables and y-axis variables, the variables are determined by the direction the object is going, anything going in a horizontal velocity/direction is a x-axis variable and anything going up or down velocity/direction is a y-axis variable. For example, a marble is pushed across a table at a velocity of 5 m/s and the height of the table is 2 meters. The velocity of the marble being pushed across the table is an x-axis variable, because its movement is horizontal (unless it's one of those funky Inspiration tables that are just there for ornamental value). The height of the table is a y-axis variable because the height of the table is the distance traveled when the marble falls off the table and the direction of the marble is then going downward.

Another way to know if something is an x or y-axis variable is by drawing out the direction of each variable. So, again, using the example of the marble this is what a drawing would look like….

The small graph that has a + in QI and a – in QII shows you what axis each variable is. So by going left or right makes a variable part of the x-axis, by going up or down makes a variable part of the y-axis. The + means that if the object is going up or moving to the right then it's velocity is positive, and the – means that if the object is going down or moving to the left then its velocity is negative. I guess this makes more sense than my big paragraph but I really don't want to delete it.

Anyway when trying to calculate the motion of a projectile you write down the given variables in a t-chart and then use the kinematic equations to find the other variables. Using the situation from before, you already know

·            the velocity of marble moving across the table (5 m/s)

·            the acceleration of the marble moving across the table (0 m/s²), because the final and initial velocity doesn't change because the marble is moving horizontally

·            the distance the marble will drop to the ground (-2 m), because it is falling downward the distance is negative

·            the initial velocity when the marble falls off the table (0 m/s), because the marble is now free falling it has no initial velocity

·            the acceleration of the marble during free fall (-9.8 m/s²), because, assuming that this place is on earth and earth's gravity pulls objects downward the acceleration is negative and equals -9.8 m/s²

With this in hand you can now fill out the t-chart, it should look like this:

Also, one exception to the values of the different sets of variables is that time is a constant and that both the x and y-axis share it.

To find the rest of the variables you must use the kinematic equations, here is how I found each variable….

Find the final velocity after the marble hits the ground.

Finding the time it took the marble to fall to the ground.

Finding the horizontal range as the marble falls to the ground.