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
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?
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.