Question 1028734
{{{ h(t) = -16t^2 + 6t + 12 }}}
(a)
You hit the water when {{{ h(t) = 0 }}}, which
is 12 ft below the diving board
{{{ 0 = -16t^2 + 6t + 12 }}}
you can use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -16 }}}
{{{ b = 6 }}}
{{{ c = 12 }}}
{{{ t = (-6 +- sqrt( 6^2 - 4*(-16)*12 )) / (2*(-16)) }}}
{{{ t = (-6 +- sqrt( 36 + 768 )) / (-32) }}}
{{{ t = (-6 +- sqrt( 804 )) / (-32) }}}
{{{ t = (-6 - 28.3549 ) / (-32) }}}
{{{ t = ( -34.3549 ) / ( -32 ) }}}
{{{ t = 1.0736 }}}
You hit the water in 1.07 sec
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(b)
The maximum height is when:
{{{ t[max] = -b/(2a) }}}
{{{ t[max] = -6/(2*(-16) ) }}}
{{{ t[max] = 3/16 }}}
Plug this back into equation
{{{ h(t) = -16t^2 + 6t + 12 }}}
{{{ h[max] = -16*(3/16)^2 + 6*(3/16) + 12 }}}
{{{ h[max] = -.5625 + 1.125 + 12 }}}
{{{ h[max] = 12.5625 }}}
The maximum height above the pool is 12.56 ft
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check:
here's the plot:
{{{ graph( 400, 400, -2, 2, -3, 16, -16x^2 + 6x + 12 ) }}}