Question 836334
If I say:
{{{ h(t) = -16t^2 + b*t }}}
One of the roots is {{{ t = 0 }}}
{{{ h(0) = 0 }}}
{{{ 0 = -16*0^2 + b*0 }}}
and, the other root is:
{{{ t = 3.6 }}}
{{{ h(3.6) = 0 }}}
{{{ 0 = -16*3.6^2 + b*3.6 }}}
{{{ 0 = -207.36 + 3.6b }}}
{{{ 3.6b = 207.36 }}}
{{{ b = 57.6 }}}
-----------------
The maximum height is reached when:
{{{ t[max] = -b/(2a) }}} where
{{{ a = -16 }}}
{{{ b = 57.6 }}}
{{{ t[max] = -57.6/(-32) }}}
{{{ t[max] = 1.8 }}}
and
{{{ h(t) = -16t^2 + 57.6*t }}}
{{{ h(1.8) = -16*1.8^2 + 57.6*1.8 }}}
{{{ h(1.8) = -51.84 + 103.68 }}}
{{{ h(1.8) = 51.84 }}}
The greatest height reached is 51.84 ft
Here's the plot:
{{{ graph( 400, 400, -1, 5, -10, 60, -16x^2 + 57.6x ) }}}