10-15 minutes to work on finishing
the trajectory problems (then go
over a few of them).
 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)
What is the difference between these
two images?
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
Projectile Motion Equations
Gun Pointing Up
Gun Pointing Down
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
y  height of victim / wound
y0  height of shooter’s location
v0  initial speed of the bullet
θ  angle of firing
Height of
t  time for bullet to travel
Shooter
g  acceleration due to gravity
(always 9.8m/s2)
How height
is affect by
vertical
velocity
How
height is
affect by
gravity
Sample Problems
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
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
1 2
y  y0  v0 sin(  )t  gt
2
1 2
y  y0  v0 sin(  )t  gt
2
1. Get into your ballistic lab groups.
2. Show me the pre-lab (EVERYONE IN THE GROUP) and
get it approved.
3. Pick up your supplies (EVERYone MUST WHERE
GOGGLES).
4. Collect your data & make observations.
5. 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!)
B. Use the trajectory method to calculate where the bullet should have
hit (height-wise) for each trial.
C. What were some observations you made during the trials?
D. Did your results match what you had expected? Why/why not?
E. 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)
I.
Background (Background on anatomy of a gun, how a gun fires,
what affects a bullet’s path) (5pts)
II. Purpose (2.5pts)
III. Experimental Setup (IV, DV, Control, Extraneous Variables)
(2.5pts)
IV. Procedures (no I, we, or you.) (5pts)
V. Data Table (5pts)
VI. Analysis (MUST BE WELL DEVELOPED) (20pts)
VII.Conclusion (review purpose of lab, whether results were expected,
what errors occurred, and how to make this lab more accurate)
(5pts)
VIII. Attached: all the lab data sheets/prelab papers (5pts)