Question 970547
I think the equation is:
{{{ h(t) = -16t^2 + 288t }}}
The {{{ t }}} coordinate of the maximum height
is at {{{ t[max] = -b / (2a) }}}
{{{ a = -16 }}}
{{{ b = 288 }}}
{{{ t[max] = -288 / (2*(-16)) }}}
{{{ t[max] = 288/32 }}}
{{{ t[max] = 9 }}} sec
It will take 9 sec to reach maximum height
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When the rocket returns to earth, {{{ h = 0 }}}
{{{ 0 = -16t^2 + 288t }}}
{{{ 0 = 16t*( -t + 18 ) }}}
{{{ t = 0 }}} ( the launch time )
{{{ t = 18 }}} ( return to earth )
In 18 sec the rocket returns to earth
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here's the plot:
{{{ graph( 400, 400, -3, 24, -150, 1500, -16x^2 + 288x ) }}}