Question

Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. Hisheight as a function of time could be modeled by the function h(t) = -16t2 + 16t + 672 , where tis the time in seconds and h is the height in feet.a) what was Jasons height after 3 secondsb) how long did it take Jason to reach his maximum height.c) what was the maximum height that Jason reached.d)after how many seconds did Jason hit the water

Answer 1

`\begin{gathered} \text{The function h(t) is as follows,} \\ h(t)=-16t^2+16t+672 \\ (a)\text{ } \\ h(3\sec )=-16(3)^2+16*3+672 \\ h(3\sec )=-144+48+672 \\ h(3\sec )=576\text{ ft} \\ (b) \\ \text{For maxi}mum\text{ height,} \\ \frac{dh}{d\text{t}}=0 \\ -32t+16=0 \\ t=2\text{ sec} \\ (c) \\ \text{The maxi}mum\text{ height is,} \\ h(2\sec )=-16*2^2+16*2+672 \\ h=640\text{ ft} \end{gathered}`