Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 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.

Answer 1

When it hits the ground, then h=0
find the xintercept or in this case the tintercepts
c=76
v=135

h=-16t^2+135t+76
use quadratic formula

ax^2+bx+c=0
x=$\frac{-b+/- \sqrt{b^2-4ac} }{2a}$

a=-16
b=135
c=76

x=$\frac{-135+/- \sqrt{135^2-4(-16)(76)} }{2(-16)}$
x=$\frac{-135+/- \sqrt{18225+4864} }{-32}$
x=$\frac{-135+/- \sqrt{23089} }{-32}$
aprox
x=-0.5297 or 8.967
exclude the negative root since you can't have negative time

means that it takes 8.97 seconds to hit the ground