To find the maximum height, we need to find the vertex of the parabolic function h = -16t^2 + 120t + 10. The vertex occurs at t = -b/2a, where a = -16 and b = 120.
t = -b/2a = -(120)/(2(-16)) = 3.75
So the boulder reaches its maximum height after 3.75 seconds. To find the maximum height, we substitute this value of t into the function:
h = -16(3.75)^2 + 120(3.75) + 10 ≈ 235.00
So the boulder reaches a maximum height of 235.00 feet after 3.75 seconds. The answer is A.
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. How long does it take to reach maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
A. Reaches a maximum height of 235.00 feet in 3.75 seconds.
B. Reaches a maximum height of 10.00 feet in 7.50 seconds.
C. Reaches a maximum height of 7.58 feet in 3.75 seconds.
D. Reaches a maximum height of 15.16 feet in 7.5 seconds.
1 answer