Homework – Free Fall and Projectiles Name: ____ANSWER KEY______ 1. A ball is dropped from the top of a 20 meter building. How long does it take for the ball to reach the ground?

t = 2 s What is the velocity of the ball when it reaches the ground? (Be careful on this one)

v = -20 m/s What is the speed of the ball when it reaches the ground?

speed = 20 m/s 2. The same ball is dropped from the top of a 40 meter building. How long does it take for the ball to reach the ground?

t = 2.83 s What is the velocity of the ball when it reaches the ground? (Be careful on this one too)

v = -28.3 m/s What is the speed of the ball when it reaches the ground?

speed = 28.3 m/s 3. In problem 2 the ball was dropped from twice the height as the same ball in problem 1. Answer the following questions about the time it took for the ball to reach the ground: Did the time increase or decrease with increased height?

increase By what factor did the time increase or decrease?

√2 How is this factor related to the difference in the height of the buildings? y = ½ a t2

4. A ball is thrown straight up with a velocity of 5 m/s. How long does it take for the ball to reach its maximum height?

t = 0.5 s How long does it take for the ball to return to its starting position?

t = 1 s How are the answers for the previous two problems related?

time up = time down so time to return is double the time to the max height 5. A red ball and blue ball are dropped from the top of a very tall building. However, the blue ball is dropped 1 second after the red ball. How much further is the red ball from the blue ball after 1 second?

red y = -5 m and blue y = -0 m so red is 5 m further down How much further is the red ball from the blue ball after 2 seconds?

red y = -20 m and blue y = -5 m so red is 15 m further down Is there a pattern to the distance between the red and blue ball at each second? Explain.

yes, every second the distance between increases by 10 m How much faster is the red ball moving than the blue ball after 2 seconds? 10 m/s How much faster is the red ball moving than the blue ball after 3 seconds? 10 m/s Is there a pattern to the difference in velocities between the two balls at each second? Explain. yes, 10 m/s

0 0 0 0 5 1 20 5 20 2 40 20 45 3 60 45 80 4 80 80 125 5 100 125

They hit at the same time.

There is no effect. Motion in the two dimensions is independent of one another.

250 m 125 m

20 m/s

20 m/s 20 m/s

20 m/s

10 m/s

20 m/s

30 m/s

40 m/s

a) Δy = - 80 m b) Δx = 80 m

Δx = 64 m