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September 20, 2014

Homework Help: MATH

Posted by TB on Sunday, June 24, 2007 at 10:33am.

The height h in feet of an object after t seconds is given by the function h=-16t^2+60t+9....
How long will it take the object to hit the ground? Round your answer to the nearest thousandth....

when it hits the ground, h is zero. So you have a quadratic equation. Use the quadratic equation to solve...
-16t^2+60t+9=0

The height h in feet of an object after t seconds is given by the function h=-16t^2+60t+9....
How long will it take the object to hit the ground? Round your answer to the nearest thousandth

The formula you give is for determining the height reached by an object when launched from a height of 9 feet above the ground, h = 9 + Vot - gt^2 where h == the maximum height, Vo = the initial velocity and g = the acceleration due to gravity, 32 fps^2.

Your formule implies a Vo of 60 fps.

The time to reach the maximum height derives from Vf = Vo - gt or 0 = 60 - 32t making t = 1.875 sec.

The height reached is h = 9 + 60(1.875) - 16(1.875^2) = 65.25 ft.

The time to fall back down to the ground, 9 feet below the launch height of 9 feet, derives from
74.25 = 0 + 16t^2 making t = 2.15 sec.

The total time of flight is therefore 4.029 sec.

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