Question 921182
The basketball can't go through the basket while
it is on the way up ( y increasing ). It has to reach it's
maximum height, and then go through the basket
on the way down ( y decreasing )
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{{{ y = -16t^2 + 18t + 7 }}}
{{{ 10 = -16t^2 + 18t + 7 }}}
{{{ -16t^2 + 18t - 3 = 0 }}}
Use the quadratic formula
{{{ t = ( -b +- sqrt(  b^2 - 4*a*c )) / (2*a) }}}
{{{ a = -16 }}}
{{{ b = 18 }}}
{{{ c = -3 }}}
{{{ t = ( -18 +- sqrt(  18^2 - 4*(-16)*(-3) )) / (2*(-16)) }}}
{{{ t = ( -18 +- sqrt(  324 - 192 )) / (-32) }}}
{{{ t = ( -18 +- sqrt(  132 )) / (-32) }}}
{{{ t = ( -18 + 11.489 ) / (-32) }}}
{{{ t = .2035 }}} sec
This is when the basketball is on the way up, just after
it leaves the shooters hand
The other value for {{{ t }}} should be when it is going
through the basket on the way down
{{{ t = ( -18 - 11.489 ) / (-32) }}}
{{{ t = 29.489/32 }}}
{{{ t = .9215 }}} sec
Rounded off:
{{{ t = .92 }}} sec
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Here's the plot:
{{{ graph( 400, 400, -.5, 1.5, -1, 14, -16x^2 +18x + 7 ) }}}