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Trajectory and Projectile Motion

- 10-15 minutes to work on finishing the trajectory problems (then go over a few of them).

Trajectory and Projectile Motion

- In groups brainstorm some ideas about this trajectory method:- How is the trajectory method used pretty accurate?- Where does the trajectory method breakdown? (where does it have problems)

Projectile Motion (Physics of Bullets)

Describes the motion of an object in TWO dimensions

Neglect air resistance to make it simpler

Projectile Motion

The ball is in free fall vertically and moves at constant speed horizontally!!!

Projectile Motion Basics

- Every moving object has horizontal & vertical velocity.
- Vertical velocity is changed by force of gravity.
- Horizontal velocity stays the same.

Projectile Motion

- As a cannon is fired upward, the horizontal velocity stays the same.
- Gravity causes the bullet to arc (which creates the parabola)

Projectile Motion

- The angle of firing affects the path of the bullet over a period of time.

Projectile Motion Equations

Gun Pointing Up

Gun Pointing Down

y height of victim / wound (m)

y0 height of shooter’s location (m)

v0 initial speed of the bullet (m/s)

θ angle of firing

t time for bullet to travel (s)

g acceleration due to gravity (always 9.8m/s2)

Projectile Motion Equations

Gun Pointing Up

Gun Pointing Down

y height of victim / wound

y0 height of shooter’s location

v0 initial speed of the bullet

θ angle of firing

t time for bullet to travel

g acceleration due to gravity (always 9.8m/s2)

How height is affect by gravity

How height is affect by vertical velocity

Height of Shooter

Sample Problems

1. A sharpshooter is located in a tree. The sharpshooter fires down at a 30 degree angle. It takes the bullet 0.5s to hit the victim’s shoulder at 1.2m high. The speed of the bullet was 62m/s. How high up is the sharpshooter?

1.2 = y0 - 62sin(30)x(0.5) – (0.5)(9.8)(0.5)2

1.2 = y0 – 15.5 – 1.225

1.2 = y0 – 17.725

18.925m = y0

Sample Problems

2. A sharpshooter is located in a tree 15m tall. The sharpshooter fires down at a 25 degree angle. It takes the bullet 0.5s to hit the victim’s shoulder (located at 1.5m high). What is the speed of the bullet as it leaves the gun?

1.5 = 15 - v0sin(25)x(0.5) – (0.5)(9.8)(0.5)2

1.5 = 15 – 0.211v0– 1.225

-12.275 =-0.211v0

58.2m/s =v0

Sample Problems

3. A sharpshooter fires a gun from the ground at a height of 2.0m and angle of 45degrees up. It takes the bullet 1.2s to hit the victim located in a building 120m high. What is the speed of the bullet as it leaves the gun?

120 = 2.0 + v0sin(45)x(1.2) – (0.5)(9.8)(1.2)2

120 = 2.0 + 0.849v0– 7.056

125.056 =0.849v0

147.3m/s =v0

Sample Problems

4. A sharpshooter is located in a tree 25m tall. The tree is located 15m away from the victim. It takes the bullet 0.1s to hit the victim’s shoulder (located at 1.2m high). What is the speed of the bullet as it leaves the gun?

1.2 = 25 - v0sin(θ)x(0.1) – (0.5)(9.8)(0.1)2

1.2 = 25 – 0.1v0sin(θ)– 0.049

-23.751 =-0.1v0sin(θ)

-23.751 =-0.1v0sin(59) = -0.1x0.857v0

277.1m/s=v0

Ballistics Lab

- Get into your ballistic lab groups.
- Show me the pre-lab (EVERYONE IN THE GROUP) and get it approved.
- Pick up your supplies (EVERYone MUST WHERE GOGGLES).
- Collect your data & make observations.
- Cleanup and put all materials away.
- *When done, you can work on your projectile motion practice problems!

Analysis of Lab (Most Important Section)

- A. For each trial of data, calculate the initial speed of the gun. Find an average for the initial speed (v0). (Be sure to show your work!)
- Use the trajectory method to calculate where the bullet should have hit (height-wise) for each trial.
- What were some observations you made during the trials?
- Did your results match what you had expected? Why/why not?
- What are some factors that could have affected the outcome of your results? Explain these factors.

Ballistics Lab Report – DUE NEXT WEDNESDAY(LAB GRADE – 50 pts)

- Background (Background on anatomy of a gun, how a gun fires, what affects a bullet’s path) (5pts)
- Purpose(2.5pts)
- Experimental Setup (IV, DV, Control, Extraneous Variables) (2.5pts)
- Procedures(no I, we, or you.)(5pts)
- Data Table(5pts)
- Analysis (MUST BE WELL DEVELOPED) (20pts)
- Conclusion (review purpose of lab, whether results were expected, what errors occurred, and how to make this lab more accurate) (5pts)
- Attached: all the lab data sheets/prelab papers (5pts)

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