Question 79393
When a ball is thrown, its height in feet h after t seconds is given by the equation h=vt-16t, where v is the initial upwards velocity in feet per second. If v=36 feet per second, find all values of t for which h=19 feet. Do not round any intermediate steps. Round your answers to 2 decimal places. 
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I think the equations would be: -16t^2 + 36t = 19
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-16t^2 + 36t - 19 = 0
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Find the value of t using the quadratic formula: a=-16; b=36; c=-19
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
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{{{t = (-36 +- sqrt( 36^2 - 4*-16*-19 ))/(2*-16) }}}
:
{{{t = (-36 +- sqrt(1296 - 1216 ))/(-32) }}}
:
{{{t = (-36 +- sqrt(80 ))/(-32) }}}
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Two solutions:
{{{t = (-36 + 8.94)/-32}}}
{{{t = (-27.06)/(-32)}}}
t = +.85 sec (At 19' on the way up)
and
{{{t = (-36 - 8.94)/-32}}}
{{{t = (-44.94)/(-32)}}}
t = 1.40 sec (At 19' on the way down)
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Would look like this:
{{{ graph( 300, 200, -2, 4, -5, 30, -16x^2 + 36x ) }}}
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Note that it shows about 19 ft at about .85 sec and 1.4 sec
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Has this helped you find your way?