Susan throws a softball upward into the air at a speed of 32 feet per second from a 40-foot platform. The height of the ball after seconds is given by the function h(t)= -16t² + 32t + 40

Question

When does the softball reach its maximum height

What is the maximum height reached by the softball and at what time does this maximum height occur?

Answer 1

The maximum height reached by the softball can be found by looking at the vertex of the parabolic function h(t) = -16t^2 + 32t + 40.

The formula for finding the x-coordinate of the vertex of a parabola in the form ax^2 + bx + c is given by x = -b/(2a). In this case, a = -16 and b = 32.

x = -32/(2*-16) = -32/-32 = 1

So, the softball reaches its maximum height at t = 1 second.

To find the maximum height, plug t = 1 into the function h(t):

h(1) = -16(1)^2 + 32(1) + 40 = -16 + 32 + 40 = 56

Therefore, the maximum height reached by the softball is 56 feet at t = 1 second.