Question

A rocket is launched from atop a 74-foot cliff with an initial velocity of 113 ft/s. The height of the rocket above the ground at time t is given by h=16t^2+113t+74. When will the rocket hit the ground after it is launched? Round to the nearest tenth of a second.

Answer 1

9514 1404 393

Answer:

7.7 seconds

Explanation:

The solution is given by the quadratic formula.

For ax² +bx +c = 0, the roots are ...

x = (-b±√(b²-4ac))/(2a)

We want the positive root, so ...

x = (-113 -√(113² -4(-16)(74)))/(2(-16)) = (113 +√17505)/32 ≈ 7.6658

The rocket will hit the ground about 7.7 seconds after it is launched.