Question

A ball is thrown directly upward from an initial height of 200 feet with an initial velocity of 96 feet per second. The height of the ball thrown is given by the function h(t) = -16t² + 96t + 200. What is its maximum height?

A) 272 feet
B) 312 feet
C) 344 feet
D) 376 feet

Answer 1

The maximum height of the ball thrown is 344 feet.

Step-by-step explanation:

To find the maximum height of the ball thrown, we need to find the vertex of the quadratic function h(t) = -16t² + 96t + 200. The vertex of a quadratic function is given by the formula t = -b/2a, where a = -16 and b = 96. Substituting these values into the formula, we get t = -96/(-32) = 3 seconds. To find the maximum height, substitute t = 3 into the function h(t). So, h(3) = -16(3)² + 96(3) + 200 = 344 feet. Therefore, the maximum height of the ball is 344 feet.