Question 1099275
{{{ h(t) = -4.9t^2 + 25t + 20 }}}
When will the height of the rock be {{{ h(t) = 7 }}} ?
{{{ 7 = -4.9t^2 + 25t + 20 }}}
{{{ -4.9t^2 + 25t + 13 = 0 }}}
Use the quadratic formula
{{{ t = ( -b +-sqrt( b^2 - 4*a*c ) ) / (2a) }}}
{{{ a = -4.9 }}}
{{{ b = 25 }}}
{{{ c = 13 }}}
{{{ t = ( -25  +-sqrt( 625 - 4*(-4.9)*13 )) / (2*(-4.9) ) }}}
{{{ t = ( -25 +-sqrt( 625 + 254.8 )) / (-9.8) }}}
{{{ t = ( -25 +-sqrt( 879.8 )) / (-9.8) }}}
{{{ t = ( -25 - 29.661 ) / ( -9.8 ) }}} ( use negative square root to get positive time )
{{{ t = 54.661/9.8 }}}
{{{ t = 5.578 }}} sec
The rock will be 7 meters from the water in 5.58 sec
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check answer:
{{{ 7 = -4.9*5.58^2 + 25*5.58 + 20 }}}
{{{ 7 = 152.568 + 139.5 + 20 }}}
{{{ 7 = 6.932 }}}
I think error is due to rounding off.
check the math & get another opinion if needed