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 = -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.
a. Substitute the values into the equation:
0 = -16t^2 + 135t + 76
b. Using the quadratic formula, we have:
t = [-b ± √(b^2 - 4ac)] / 2a
Plugging in the values for a, b, and c from the equation:
t = [-135 ± √(135^2 - 4*(-16)*76)] / 2*(-16)
t = [-135 ± √(18225 + 4864)] / -32
t = [-135 ± √23089] / -32
t = [-135 ± 152.08] / -32
Therefore, the two values of t are:
t = (-135 + 152.08) / -32 ≈ 0.54 seconds
t = (-135 - 152.08) / -32 ≈ -16.68 seconds
Since time cannot be negative, the rocket will hit the ground approximately 0.54 seconds after being launched.