Question

A ball with mass m kg is thrown upward with initial velocity 28 m/s from the roof of a building 17 m high. Neglect air resistance Use g = 9.8 m/s. Round your answers to one decimal place. (a) Find the maximum height above the ground that the ball reaches. meters (b) Assuming that the ball misses the building on the way down, find the time that it hits the ground. Fend Click If you would like to Show Work for this question: Open Show Work LINK TO TEXT

Answer 1

a. At its maximum height, the ball has zero vertical velocity, so

$-\left(28\dfrac{\rm m}{\rm s}\right)^2=2(-g)(y_{\rm max}-17\,\mathrm m)$

$\implies y_{\rm max}=57\,\mathrm m$

b. The ball's height in the air $y$ at time $t$ is given according to

$y=17\,\mathrm m+\left(28\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2$

Solve for $t$ when $y=0$:

$17+28t-4.9t^2=0\implies t\approx6.3\,\mathrm s$