Question 731857
The equation should be:
{{{ h(t) = -16t^2 + 80t + 96 }}}
The object will hit the ground when
{{{ h(t) = 0 }}} , so
{{{ 0 = -16t^2 + 80t + 96 }}}
Divide both sides by {{{ 16 }}}
{{{ 0 = -t^2 + 5t + 6 }}}
Using the quadratic equation:
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -1 }}}
{{{ b = 5 }}}
{{{ c = 6 }}}
{{{ t = (-5 +- sqrt( 5^2 - 4*(-1)*6 )) / (2*(-1)) }}}
{{{ t = (-5 +- sqrt( 25 + 24 )) / (-2) }}}
{{{ t = (-5 +- sqrt( 49 )) / (-2) }}}
{{{ t = ( -5 - 7 ) / (-2) }}} ( can't use the (+) square root, gives negative t )
{{{ t = 6 }}}
The object hits the ground in 6 sec
Here's the plot:
{{{ graph( 400, 400, -2, 7, -10, 220, -16x^2 + 80x + 96 ) }}}