Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 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.
Accepted Solution
A:
Here the vertical motion formula is h = -16t^2 + 116t + 101 (feet)
How long will it take for the rocket to rise, stop rising, start falling and then his the ground? To find this, set h = 0 and solve for t. Omit negative results, if any.
-16t^2 + 116t + 101 = 0.
Since the solutions are unlikely to be "nice" numbers (integers), let's use the quadratic formula to solve this equation for t:
-116 plus or minus sqrt(116^2 - 4(-16)(101) ) t = ---------------------------------------------------------------- 2(-16) -116 plus or minus sqrt(19920) = --------------------------------------------- -32 -116 plus or minus 141.1 = ----------------------------------- -32
= -25.1/(-32) (discard) and t = -116 - 141.1 ------------------ -32
t = 8.03.
The rocket will hit the ground 8.03 seconds after it is launched.