Question 763222
W.E.C. will land in the riven when {{{ h = 0 }}}
when his height is zero
{{{ v[0] = 4 }}} ft/sec
{{{ s = 120 }}}
{{{ h(t) = -16t^2 + v[0]*t + s }}}
{{{ 0 = -16t^2 + 4t + 120 }}}
{{{ 0 = -4t^2 + t + 30 }}}
{{{ t = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -4 }}}
{{{ b = 4 }}}
{{{ c = 30  }}}
{{{ t = ( -1 +- sqrt( 1^2 - 4*(-4)*30 )) / (2*(-4)) }}}
{{{ t = ( -1 +- sqrt( 1 + 480 )) / (-8) }}}
{{{ t = ( -1 - sqrt( 481 )) / (-8) }}}
{{{ t = ( -1 - 21.932) / (-8) }}}
{{{ t = -22.932 / ( -8 ) = 2.866 }}}
In 2.866 sec, he lands in the river
Here's the plot:
{{{ graph( 400, 400, -1, 4, -20, 140, -16x^2 + 4x + 120 ) }}}
The time at {{{ h = 0 }}} looks about right