A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h=-16t^2+148t+30. What is the boulder’s maximum height? How long does it take the boulder to reach its maximum height? Round to the nearest hundredth, if necessary.

Answer 1

To find the boulder's maximum height, we need to find the vertex of the parabolic function h.

First, we can rewrite the function in vertex form:

h = -16(t - 4.625)^2 + 833.625

where 4.625 is the time it takes for the boulder to reach its maximum height and 833.625 is the maximum height in feet.

To find the time it takes for the boulder to reach its maximum height, we can use the formula:

t = -b/2a

where a = -16 and b = 148.

t = -148/(2(-16)) = 4.625 seconds

To find the maximum height, we substitute this value of t into the original function:

h = -16(4.625)^2 + 148(4.625) + 30 = 833.625 feet

Therefore, the boulder reaches a maximum height of 833.625 feet and it takes 4.63 seconds to reach this height.