Question

Use the quadratic formula to solve the equation.

If necessary, round to the nearest hundredth.
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 = −16t2 + 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.

A. 0 = −16t2 + 99t + 122; 8.4 s

B. 0 = −16t2 + 99t + 122; 0.7 s

C. 0 = −16t2 + 122t + 99; 8.4 s

D. 0 = −16t2 + 122t + 99; 0.7 s

Answer 1

the formula is -16t^2 + 122t + 99

Solving for t gives t = 8.36 seconds

Its C

Answer 2

When you put the given numbers (v=122, c=99) into the vertical motion formula, you get
0 = -16t² + 122t + 99

Solving that using the quadratic formula for a=-16, b=122, c=99, you get
t = (-b±√(b²-4ac))/(2a)
t = (-122 ±√(122²-4·(-16)·99))/(2·(-16))
t = (122 ±√21220)/32
t = 3.8125 ± √20.72265625
t ≈ -0.7 or 8.4

The appropriate choice is ...
C. 0 = -16t² + 122t + 99; 8.4 s