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=-16t^2+120t+10. how long does it take to reach its maximum height? what is the boulders maximum height? round to the nearest hundredth, if necessary.

Answer 1

To find the maximum height, we need to find the vertex of the parabola given by the function h(t) = -16t^2 + 120t + 10.

The time required to reach maximum height occurs at the t-value of the vertex, given by:

t = -b/2a = -120 / (2*(-16)) = 3.75 seconds.

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

h(3.75) = -16(3.75)^2 + 120(3.75) + 10 = 212.5 feet.

Therefore, the boulder reaches its maximum height of 212.5 feet after 3.75 seconds.