Question 615575
{{{  H(t)=720t-16t^2 }}}
Find 2 points where the height of the rocket is zero
One point is at (0,0) because
{{{  H(t)=720*0-16*0^2 }}}
{{{ H(0) = 0 }}}
Now set {{{ H(t) = 0 }}}
{{{ 0 = 720t - 16t^2 }}}
{{{ 0 = t*( 720 - 16t) }}}
This is true if {{{ t = 0 }}} or if
{{{ 720 - 16t = 0 }}}
{{{ 16t = 720 }}}
{{{ t = 45 }}}
So, the 2nd point is at (45,0)
The midpoint of this parabola is at {{{ ( 0 + 45 ) / 2 = 22.5 }}} sec
The find the height at this time,
{{{ H(22.5) = 720*22.5 - 16*22.5^2 }}}
{{{ H(22.5) = 16200 - 8100 }}}
{{{ H( 22.5) = 8100 }}}
The maximum height is 8,100 ft
Here's the plot where height is in hundreds of feet
{{{ graph( 400, 400, -5, 50, -15, 100, 7.2x - .16x^2 ) }}}