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A baseball is thrown upward at a velocity of 36 feet per second from a height of 7 feet. The equation to represent the height (h) after t seconds is h=−16t2+36t+7. How long before the ball hits the ground? (Round to the nearest hundredth of a second.)

Bunnie  Nov 29, 2017
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h  =  -16t2 + 36t + 7

 

We want to find the time when the height is  0  .

So plug in  0  for  h  and solve for  t .

 

0  =  -16t2 + 36t + 7       Let's use the quadratic formula to solve this.

 

t  =  \(\frac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}\)

 

t  =  \(\frac{-36\pm\sqrt{1296+448}}{-32}\)

 

t  =  \(\frac{-36\pm\sqrt{1744}}{-32}\)

 

t  =  \(\frac{-36+\sqrt{1744}}{-32}\)  ≈  -0.18              or              t  =  \(\frac{-36-\sqrt{1744}}{-32}\)  ≈  2.43

 

It will take about  2.43 seconds for the ball to hit the ground.

hectictar  Nov 29, 2017

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