1. Do Now Heading: Projectile Motion and Ramps
Jackie wants to know how high her apartment window is off of the ground. So she decides to drop a ball from rest out of her window and time the fall.
She finds out that it takes 30 seconds for the ball to hit the ground.
What is final velocity of the ball when it hits the ground.
What is the average velocity of the ball?
How high is her apartment window?

2. Two types of problems that are solved exactly like free fall problems
Projectile Motion
Ball Down A Ramp

3. The Three Equations
𝒅= 𝒗 𝒂𝒗𝒈 𝒙 𝒕
𝒗 𝒇 = 𝒗 𝒊 +𝒂 ∗ 𝒕
𝒗 𝒂𝒗𝒈 = 𝒗 𝒇 + 𝒗 𝒊 𝟐

4. Rolling Down a Ramp A ball is rolled down a ramp from rest
( vi = 0 m/s). It takes the ball 10 seconds to roll to the bottom.
What is the final velocity of the ball?
What is the average velocity of the ball?
What is the length of the ramp?

5. Rolling Down a Ramp A ball is rolled down a ramp from rest
( vi = 5 m/s). It takes the ball 15 seconds to roll to the bottom.
What is the final velocity of the ball?
What is the average velocity of the ball?
What is the length of the ramp?

6. Rolling Down a Ramp
A ball is rolled down a ramp from rest ( vi = 0 m/s). The length of the ramp is 20 meters.
a) What is the average velocity of the ball?
b) How long did it take the ball to reach the bottom of the ramp?

8. Free Fall
A man throws a ball in the air with an initial velocity ( vi = 60 m/s).
What is the acceleration of the ball during its path?
What is the velocity of the ball at the very top of its path?
What is the velocity of the ball when it comes back down?
How long does it take for the ball to complete this path?

9. Free Fall
A man throws a ball in the air with an initial velocity ( vi = 20 m/s).
What is the velocity of the ball at the very top of its path?
What is the velocity of the ball when it comes back down?
How long does it take for the ball to complete this path?
How high up does the ball go before it starts to come down?

10. Free Fall
A man throws a ball in the air. The ball is in the air for 12 seconds before it hits the ground.
What is the acceleration of the ball during its path?
How many seconds does it take for the ball to get to the top of the arch.
What is the velocity of the ball at the top of the arch
What is the velocity of the ball when it comes back down?
How high up does the ball go before it starts to come back down?