Question 345461
When the ball hits the ground, {{{h = 0}}}, so
{{{ h = -16t2 + 16t + 320 }}}
{{{ 0 = -16t2 + 16t + 320 }}}
Divide both sies by {{{16}}}
{{{-t^2 + t + 20 = 0}}}
Use quadratic equation to find {{{t}}}
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -1}}}
{{{b = 1}}}
{{{c = 20}}}
{{{t = (-1 +- sqrt( 1^2-4*(-1)*20 ))/(2*(-1)) }}}
{{{t = (-1 +- sqrt( 1 + 80 ))/(-2) }}}
{{{t = (-1 +- sqrt( 81 ))/(-2) }}}
Take the negative square root in order
to get a positive answer:
{{{t = (-1 -9)/(-2)}}}
{{{t = 10/2}}}
{{{t = 5}}} sec
The ball will hit the ground in 5 sec
check answer:
{{{-t^2 + t + 20 = 0}}}
{{{-5^2 + 5 + 20 = 0}}}
{{{-25 + 5 + 20 = 0}}}
{{{0 = 0}}}
OK