1. Purdue University, Physics 220
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Lecture 6
Purdue University, Physics 220

2. Purdue University, Physics 220
Lecture 06
Projectile Motion
Textbook Sections 4.2
Lecture 6
Purdue University, Physics 220

3. Purdue University, Physics 220
2-Dimensions
X and Y are
INDEPENDENT!
Break 2-D problem into two
1-D problems y x
Lecture 6
Purdue University, Physics 220

4. Relative Velocity
We often assume that our reference frame is attached to the Earth.
Give examples when the reference frame is moving at a constant velocity with respect to the Earth:
Lecture 6

5. Purdue University, Physics 220
Relative Velocity
We often assume that our reference frame is attached to the Earth. What happen when the reference frame is moving at a constant velocity with respect to the Earth?
The motion can be explained by including the relative velocity of the reference frame in the description of the motion.
The ground velocity of an airplane is the vector sum of the air velocity and the wind velocity. Using the air as the intermediate reference frame, ground speed is:
Example airplane
V(PG)=V(PA) +V(AG)
Lecture 6
Purdue University, Physics 220

6. Inertial Frame of Reference
Any reference frame in which Newton’s laws are valid is called an inertial frame of reference
(nonaccelerating reference frame)
Lecture 3
Purdue University, Physics 220

7. Purdue University, Physics 220
iClicker
You are on a train traveling 40 mph North. If you walk 5 mph sideways across the car (W), what is your speed relative to the ground?
A) >40 mph B) 40 mph C) <40 mph
Answer: C
40 mph N + 5 mph W = 40.3 mph NW 5  40
Lecture 6
Purdue University, Physics 220

8. Purdue University, Physics 220
Exercise
Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race?
A) Ann
B) Beth
C) Carly
correct q x y
t = d / vy
Ann vy = v cos(q)
Beth vy = v
Carly vy = v cos(q)
Add Calculation. What angle to get straight across river?
A B C
Lecture 6
Purdue University, Physics 220

9. Purdue University, Physics 220
Exercise
What angle should Ann take to get directly to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph? q x y
VAnn,ground = Vann,water+Vwater,ground
Add Calculation. What angle to get straight across river? degrees
x-direction:
sin(q) = |Vwater,ground|/ |Vann,water|
sin(q) = 3/5
A B C
Lecture 6
Purdue University, Physics 220

10. Velocity in Two Dimensions
A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s.
What is the magnitude of the change in velocity? y x
x-direction
vix = 5 m/s
vfx = 3 m/s cos(25)
Dvx = 3cos(25)–5 =-2.28m/s
y-direction
viy = 0 m/s
vfy = 3 m/s sin(25)
Dvy = 3sin(25)=+1.27 m/s
ACT A) 0 B) 2 C) 2.6 D)3 E) 5
3 m/s
5 m/s
Lecture 6
Purdue University, Physics 220

11. Acceleration in Two Dimensions
A ball is rolling on a horizontal surface at 5 m/s. It then rolls up a ramp at a 25 degree angle. After 0.5 seconds, the ball has slowed to 3 m/s.
What is the average acceleration? y x
x-direction
y-direction
3 m/s
5 m/s
Lecture 6
Purdue University, Physics 220

12. Kinematics in Two Dimensions
x = x0 + v0xt + 1/2 axt2
vx = v0x + axt
vx2 = v0x2 + 2ax x
y = y0 + v0yt + 1/2 ayt2
vy = v0y + ayt
vy2 = v0y2 + 2ay y
x and y motions are independent!
They share a common time t
Lecture 6
Purdue University, Physics 220

13. Purdue University, Physics 220
Projectile Motion
x-direction: ax = 0
y-direction: ay = -g
y = y0 + v0y t - ½ gt2
vy = v0y – g t
vy2 = v0y2 – 2 g y
x = x0 + v0x t
vx = v0x
Lecture 6
Purdue University, Physics 220

14. Velocity of a Projectile
Velocity components of a projectile
Lecture 6
Purdue University, Physics 220

15. Purdue University, Physics 220
Lecture 6
Purdue University, Physics 220

16. Independence of the Vertical and Horizontal motion of Projectiles
Lecture 6
Purdue University, Physics 220

17. Purdue University, Physics 220
The Range of a Kickoff
A place-kicker kicks a football at an angle of =400 above the horizontal axis. The initial speed of the ball is v0=22 m/s. Ignore air resistance and find the range R that the ball attains.
v0=22m/s
=400 H R
Lecture 6
Purdue University, Physics 220

18. Purdue University, Physics 220
The Range of a Kickoff
Use the equations
y = y0 + v0yt - 1/2 gt2
vy = v0y - gt
vy2 = v0y2 - 2g y
x = x0 + v0xt
vx = v0x
The range is a characteristic of the horizontal motion
You need v0x and v0y but you have been given v0
v0x = v0cos  =
(22m/s)cos 400 = 17 m/s
v0x 
v0y v0
Lecture 6
Purdue University, Physics 220

19. Purdue University, Physics 220
The Range of a Kickoff
We could be done if we know the time of flight of the kickoff
The time of flight can be determined from y equations. For example the time to get to height H is
v0x 
v0y v0
v0y =v0sin =
(22m/s)sin 400=14 m/s
Therefore the time to determine the range is 2.9 s
The range depends on the angle  at which the football is kicked. Maximum range is reached for =450
Lecture 6
Purdue University, Physics 220

20. Purdue University, Physics 220
Range of a Projectile
Lecture 6
Purdue University, Physics 220

21. Purdue University, Physics 220
Shooting the Monkey
You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. On the other hand, you also know that the dart will not travel in a straight line, but rather in a parabolic path like any other projectile. In order to hit the monkey with the dart, where should you point the gun before shooting?
A) Right at the monkey
B) Below the monkey
C) Above the monkey
Lecture 6
Purdue University, Physics 220

22. Purdue University, Physics 220
Shooting the Monkey
y = y0 - 1/2 g t2
y = v0y t - 1/2 g t2
Dart hits the
monkey!
Lecture 6
Purdue University, Physics 220

23. Purdue University, Physics 220
iClicker
A ball is thrown into the air and follows a parabolic trajectory. At the highest point in the trajectory,
The velocity is zero, but the acceleration is not zero.
Both the velocity and acceleration are zero.
The acceleration is zero, but the velocity is not zero.
Neither the acceleration nor the velocity is zero.
Lecture 6
Purdue University, Physics 220