1. PROJECTILE MOTION

2. Projectile Examples Hockey puck Tennis ball Basketball Golf ball
Volleyball
Arrow
Shot put
Javelin
Tennis ball
Golf ball
Football
Softball
Soccer ball
Bullet
These are all examples of things that are
projected, then go off under the
influence of gravity

3. Not projectiles Jet plane Rocket
Car (unless it looses contact with ground)

4. Understanding Projectiles
 The key to understanding
projectile motion is to realize
that gravity acts vertically
 it affects only the vertical
part of the motion, not the
horizontal part of the motion

5. Demonstration
We can see that the horizontal and vertical motions are independent
The red ball falls vertically
The yellow ball was given a kick to the right.
They track each other vertically step for step and hit the ground at the same time

6. Projectile Paths In the absence of gravity a bullet
would follow a straight line forever.
With gravity it FALLS AWAY from
that straight line!

7. Shoot the Monkey

8. Sample Problem
A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the monkey, she kneels 10.0 m from the light pole,which is 5.00 m high. The tip of her gun is 1.00 m above the ground. At the same moment that the monkey drops a banana, the zookeeper shoots. If the dart travels at 50.0 m/s,will the dart hit the monkey, the banana, or neither one?

9. Sample Problem
1 . Select a coordinate system. The positive y-axis points up, and the positive x-axis points along the ground toward the pole. Because the dart leaves the gun at a height of 1.00 m, the vertical distance is 4.00 m.

10. Sample Problem
2 . Use the inverse tangent function to find the angle that the initial velocity makes with the x-axis.

11. 3 . Choose a kinematic equation to solve for time.
Sample Problem
3 . Choose a kinematic equation to solve for time.
Rearrange the equation for motion along the x-axis to isolate the unknown Dt, which is the time the dart takes to travel the horizontal distance.

12. Sample Problem
4 . Find out how far each object will fall during this time. Use the free-fall kinematic equation in both cases.
For the banana, vi = 0. Thus:
Dyb = ½ay(Dt)2 = ½(–9.81 m/s2)(0.215 s)2 = –0.227 m

13. Sample Problem
The dart has an initial vertical component of velocity equal to vi sin q, so:
Dyd = (vi sin q)(Dt) + ½ay(Dt)2
Dyd = (50.0 m/s)(sin 21.8)(0.215 s) +½(–9.81 m/s2)(0.215 s)2
Dyd = 3.99 m – m = 3.76 m

14. Sample Problem 5 . Analyze the results.
Find the final height of both the banana and the dart.
ybanana, f = yb,i+ Dyb = 5.00 m + (–0.227 m)
ybanana, f = 4.77 m above the ground

15. Sample Problem ydart, f = yd,i+ Dyd = 1.00 m + 3.76 m
ydart, f = 4.76 m above the ground
The dart hits the banana.
The slight difference is due to rounding.

16. No gravity is good for kickers

17. Newton’s First Law of Motion
“Every object continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state of motion by forces impressed upon it ”
The tendency of matter to maintain its state of motion is known as INERTIA.

18. Basketball – without gravity

19. Hitting the target – aim high, not directly at the target
BULLSEYE!

20. Path of the Projectile g falling rising Height v Distance downfield
(range)
Horizontal velocity
Vertical
velocity v
projectile

21. Horizontal Motion

22. Vertical Motion

23. Projectile motion – key points
The projectile has both a vertical and horizontal component of velocity
The only force acting on the projectile once it is shot is gravity (neglecting air resistance)
At all times the acceleration of the projectile is g = 9.8 m/s2 downward
The horizontal velocity of the projectile does not change throughout the path

24. Key points, continued
On the rising portion of the path gravity causes the vertical component of velocity to get smaller and smaller
At the very top of the path the vertical component of velocity is ZERO
On the falling portion of the path the vertical velocity increases

26. More key points
If the projectile lands at the same elevation as its starting point it will have the same vertical SPEED as it began with
The time it takes to get to the top of its path is the same as the time to get from the top back to the ground.
The range of the projectile (where it lands) depends on its initial speed and angle of elevation

28. Sample Problem
A 2.00 m tall basketball player wants to make a basket from
a distance of 10.0 m. If he shoots the ball at a 450 angle, at
what initial speed must he throw the ball so that it goes
through the hoop without striking the backboard? y x y0

29. Equations to Choose from

30. Maximum Range
When an artillery shell is fired the initial speed of the projectile depends on the explosive charge – this cannot be changed
The only control you have is over the angle of elevation.
You can control the range (where it lands) by changing the angle of elevation
To get maximum range set the angle to 45°

31. Interactive

32. The ultimate projectile: Orbit
Imagine trying to throw a rock around the world.
If you give it a large
horizontal velocity,
it will go into orbit
around the earth!