Question 839493
The problem is assuming that there is no friction on the way up.
Probably not true, but anyway:
Let {{{ h(t) }}} = the height above ground the ball reaches
The equation is:
{{{ h(t) = -16t^2 + 39t }}}
The {{{ -16t^2 }}} is due to the force of gravity pulling down
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I have to find the peak, or vertex
{{{ t[v] = -39/(2*(-16)) }}}
{{{ t[v] = 39/32 }}}
Now I need to find {{{ h( 39/32 ) }}}
{{{ h( 39/3 2) = -16*( 39/32 )^2 + 39*( 39/32 ) }}}
{{{ h( 39/32 ) = -16*( 39/32 )^2 + 39*( 39/32 ) }}}
{{{ h( 39/32 ) = -23.766 + 47.531 }}}
{{{ h( 39/32 ) = 23.765 }}}
This is short of 25 ft, so the ball doesn't hit the bell
Here's the plot:
{{{ graph( 400, 400, -5, 5, -5, 30, -16x^2 + 39x ) }}}