A rocket is launched from atop a 99-foot cliff with an initial velocity of 122 ft/s.

a. Substitute the values into the vertical motion formula h = - 16t^2 + vt + c. Let h = 0.

b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.

When t=0, h=0. Therefore c = 0

The velocity function is the derivative of the distance function, which is

v (t) = - 32t + v

When t=0, v=122

Therefore, the distance function is

h (t) = - 16t^2 + 122t

When the rocket hits the ground, h = - 99 ft.

Therefore

-16t^2 + 122t = - 99

16t^2 - 122t - 99 = 0

Solve with the quadratic formula to obtain

t = (1/32) [122 + / - (122^2 + 4*16*99) ^0.5] = 8.365 or - 0.74 s

Reject negative time.

Answer: t = 8.4 s (nearest tenth)