Question 1206150
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(a) The ball hits the ground when s, the height of the ball above the ground, is zero:<br>
{{{48t-16t^2=0}}}
{{{16(t)(3-t)=0}}}
{{{t=0}}} and {{{t=3}}}<br>
ANSWER: at 3 seconds<br>
(b) We want the height of the ball to be greater than 20 feet:<br>
It's awkward to solve the quadratic inequality.  Instead, solve an equation to find the times when the height of the ball is exactly 20 feet.  Then use common sense to get the answer.<br>
{{{48t-16t^2=20}}}
{{{16t^2-48t+20=0}}}
{{{4t^2-12t+5=0}}}
{{{(2t-5)(2t-1)=0}}}
{{{t=2.5}}} and {{{t=0.5}}}<br>
The ball is 20 feet off the ground at t=0.5 seconds and t=2.5 seconds, so it is more than 20 feet above the ground between those two times.<br>
ANSWER: between t=0.5 second and t=2.5 seconds<br>