A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = –16t2 + 120t + 10. What is the boulder’s maximum height? How long does it take to reach maximum height? Round to the nearest hundredth, if necessary.%0D%0A(1 point)

Answer 1

To find the boulder's maximum height, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 120t + 10.

The vertex of a parabolic function in the form h(t) = at^2 + bt + c is given by the formula t = -b/(2a).

In this case, a = -16 and b = 120, so t = -120/(2*(-16)) = -120/(-32) ≈ 3.75 seconds.

To find the maximum height, we substitute t = 3.75 into the height function:

h(3.75) = -16(3.75)^2 + 120(3.75) + 10 ≈ 176.25 feet.

Therefore, the boulder's maximum height is approximately 176.25 feet, and it takes approximately 3.75 seconds to reach that height.