Question

7. Alan is standing on a hill 80 feet high. He throws a baseball upward with an initial velocity of 64 feet per second. The height of the ball h(t) in terms of the time t since the ball was thrown is h(t) = -16t²+64t + 80. (a) Find the time that the ball reaches its maximum height and (b) find the maximum height

Answer 1

The ball reaches its maximum height after 2 seconds and the maximum height reached by the ball is 144 feet.

Step-by-step explanation:

(a) To find the time that the ball reaches its maximum height, we need to determine when the velocity of the ball becomes zero. The velocity of the ball is given by the derivative of the height function, which is h'(t) = -32t + 64. Setting h'(t) = 0 and solving for t gives us t = 2 seconds. Therefore, the ball reaches its maximum height after 2 seconds.

(b) To find the maximum height, we need to substitute the value of t = 2 seconds into the height function. Plugging in t = 2 in the equation h(t) = -16t²+64t + 80, we get h(2) = -16(2)²+64(2) + 80 = 144 feet. Therefore, the maximum height reached by the ball is 144 feet.