Question

A tennis player hit a tennis ball straight up into the air. The height of the ball changed according to the equation h(t)=−16t^2+64t

, where h(t) is the height in feet of the ball t seconds after the player hit it.

Which statement about the speed of the tennis ball is true?

A) The ball traveled at a constant speed of 48 feet per second during the first 3 seconds.


B) The average speed of the ball during the first 2 seconds was 64 feet per second.


C) The average speed of the ball during the first 2 seconds was 32 feet per second.


D) The ball traveled at a constant speed of 16 feet per second during the first 3 seconds.

Answer 1

The correct answer is C) The average speed of the ball during the first 2 seconds was 32 feet per second.

To find the average speed of the ball during the first 2 seconds, we need to find the change in height over the change in time. The initial height of the ball is given by h(0) = -16(0)^2 + 64(0) = 0. The height of the ball after 2 seconds is given by h(2) = -16(2)^2 + 64(2) = 64 feet.

Therefore, the change in height is:

change in height = h(2) - h(0) = 64 - 0 = 64 feet

The change in time is 2 seconds. Therefore, the average speed of the ball during the first 2 seconds is:

average speed = change in height / change in time = 64 feet / 2 seconds = 32 feet per second

So option C) The average speed of the ball during the first 2 seconds was 32 feet per second is the correct statement.