To find the time it takes for the boulder to reach its maximum height, we need to find the time when the velocity of the boulder is 0. The velocity of the boulder at any time t is the derivative of the function h(t).
Taking the derivative of the function h(t):
h'(t) = -16t^2 + 112t
Setting h'(t) = 0:
-16t^2 + 112t = 0
-16t(t - 7) = 0
t = 0 or t = 7
Since the boulder is launched upward at t = 0, the time it takes to reach the maximum height is t = 7 seconds.
To find the maximum height the boulder reaches, we need to find the height h(7):
h(7) = -16(7)^2 + 112(7)
h(7) = -784 + 784
h(7) = 0 ft
Therefore, the correct answer is c. 7 s; 30 ft
A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function mc019-1.jpg. How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
a. 3.5 s; 226 ft
Selected:b. 3.5 s; 366 ftThis answer is incorrect.
c. 7 s; 30 ft
d. 3.5 s; 618 ft
1 answer
1 answer