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.
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.