A model rocket is launched with an initial velocity of (118) feet per second fro

Question

A model rocket is launched with an initial velocity of (118) feet per second from the height of (3) feet. The function S(T) = 16t^2 + 118t + 3 models the path of the rocket where (T) represents the time, in seconds, after which the rocket is launched and (S) represents the height of the rocket at time (T). Path of Rocket How long will it take for the rocket to return to the ground? How long will it take the rocket to each its maximum height? What is the maximum height reached by the rocket? Round all answers to one decimal places

Explanation / Answer

s(t)=-16t2+118t+3

Return to ground means s(t)=0

-16t2+118t+3=0

t=7.4sec

s(t)=-16t2+118t+3

s'(t)=-32t+118

s'(t)=0

32t=118

t=118/32=3.6875sec

maximum height=-16(3.6875)2+118(3.6875)+3=220.5625feet

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