Question 1057399
The hammer has to fall 30 m
and the height, {{{ h(t) = 0 }}}
{{{ -t^2 - 2t + 30 = 0 }}}
use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -1 }}}
{{{ b = -2 }}}
{{{ c = 30 }}}
{{{ t = (-(-2) +- sqrt( (-2)^2 - 4*(-1)*30 )) / (2*(-1)) }}}
{{{ t = ( 2 +- sqrt( 4 + 120 )) / (-2) }}}
{{{ t = ( 2 +-sqrt( 124 ) ) / (-2) }}}
{{{ t = ( 2 - 11.136 ) / (-2) }}} ( I used the negative square root to make
the time, {{{ t }}}, come out positive )
{{{ t = ( -9.136 ) / (-2) }}}
{{{ t = 4.568 }}}
The hammer hits the ground in 5 sec
( rounded off )
--------------------------------------
check:
{{{ -t^2 - 2t + 30 = 0 }}}
{{{ -1*(4.568^2) - 2*4.568 + 30 = 0 }}}
{{{ -1*20.867 - 9.136 + 30 = 0 }}}
{{{ -30.003 + 30 = 0 }}}
OK -close enough