Question

A ball is kicked upward with an initial velocity of 56 feet per second. the balls height h (in feet) can be expressed as a function of time t (in seconds) by the equation h=-16t^2+56t. how much time does the ball take to return to the ground

Answer 1

check the picture below.

`\bf h=-16t^2+56t\implies \stackrel{h}{0}=8t(-2t+7) \\\\[-0.35em] ~\dotfill\\\\ 0=8t\implies 0=t\impliedby \textit{when the ball took off from the ground} \\\\[-0.35em] ~\dotfill\\\\ 0=-2t+7\implies 2t=7\implies t=\cfrac{7}{2}\implies t=3(1)/(2)\impliedby \textit{down at }3(1)/(2)~seconds`