A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after t seconds is given by the function h=-5t^2+92t+16. How long does it take to reach maximum height? What is the boulders maximum height?

Answer 1

To find the time taken to reach the maximum height, we need to first find the vertex of the parabolic function h(t)=-5t^2+92t+16.

The x-coordinate of the vertex of a parabolic function h(t) = at^2 + bt + c is given by the formula t = -b/2a. In this case, a = -5 and b = 92, so t = -92 / 2(-5) = 9.2 s.

To find the maximum height, substitute t = 9.2 into the equation for h(t):
h(9.2) = -5(9.2)^2 + 92(9.2) + 16
h(9.2) = -5(84.64) + 846.4 + 16
h(9.2) = -423.2 + 846.4 + 16
h(9.2) = 439.2

Therefore, it takes 9.2 seconds for the boulder to reach its maximum height of 439.2 meters.