1. Aim: How do we use Newton’s equation of Motion to explain the motion of a projectile launched upwards?

2. Free Fall
All bodies accelerate downwards at -9.8 m/s2 on earth regardless of mass (in the absence of air resistance). On the moon, the acceleration due to gravity is m/s2 . Since there is no air resistance on the moon, a penny and feather will hit the ground at the same time.

3. Projectiles Fired Upwards
We know three things about projectiles thrown upwards:
(Assume no air resistance)
The velocity of the projectile at its maximum height is equal to 0.

4. Projectiles Fired Upwards
2. The time it takes the object to rise is equal to the time it takes the object to fall the same amount of distance.

5. Projectiles Fired Upwards
3. The velocity with which the projectile is launched upwards will be equal in magnitude to the velocity of the projectile when it hits the ground.

6. Projectiles Fired Upwards
Note: When solving projectile motion problems in which the projectile is fired upwards, it is especially important that we make acceleration vector negative (-9.8) and the initial velocity vector is positive.

7. Example -Firing projectiles upward
An arrow is fired upwards with a velocity of 15 m/s.
How high does the arrow rise?
How long does it take the arrow to reach maximum height?
What is the total flight time?
a) m b) 1.5 s c) 3s

8. Trampoline Example
A boy jumps on a trampoline with an initial velocity of 5.0 m/s.
How high does the boy jump?
What is the total time that boy is in air for?
a) m b) 1s

9. Rocket Stomper Assume the rocket is fired straight upwards.
If the rocket reaches a maximum height of 12 m,
What is the initial velocity with which it was launched?
How long is the rocket
in the air for?
a) 15.3 m/s b)3.12 a

10. Design the Following Experiment
The only equipment you have is a timer (stopwatch). Design an experiment to determine how high the bottle rocket went. State all relevant equations you will use. Draw a sketch.

11. Problem A
Gwendolyn throws her crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.

12. Problem B
With what speed must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance. How long will object remain in air for?

13. Michael Jordan-Problem C
Michael Jordan was said to have a hang-time of 3.0 seconds (at least according to a popular NIKE commercial). Use kinematic equations to determine the height to which MJ could leap if he was wearing NIKE shoes and had a hang-time of 3.0 seconds.

14. Problem D-Hot Air Balloon
A tourist takes a trip in a hot air balloon. The hot air balloon is ascending (moving up) at a velocity of 4 m·s−1. He accidentally drops his camera over the side of the balloon's basket, at a height of 20 m. Calculate the velocity with which the camera hits the ground.

15. Problem E
A ball is thrown upwards with an initial velocity of 10 m·s−1. 1. Determine the maximum height reached above the thrower's hand. 2. Determine the time it takes the ball to reach its maximum height.