What speed will the ball hit the ground?

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To determine the speed at which the ball will hit the ground, the initial gravitational potential energy of 70J and the initial kinetic energy must be combined. The equations for kinetic energy (Ek) and gravitational potential energy (Eg) are utilized, with the assumption that all potential energy converts to kinetic energy upon impact. The initial kinetic energy is calculated using the mass of 0.24kg and the initial velocity of 20.0m/s. The final speed of the ball upon hitting the ground is calculated to be 31.4m/s, as confirmed by the book's answer. This approach effectively combines energy conservation principles to solve the problem.
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A ball has a mass of 240g. (which would be 0.24kg?) is moving through the air at 20.0m/s with a gravitational potential energy of 70J. With what speed will the ball hit the ground.

Equations:

Ek=mv^2/2 (kinetic energy)
Eg=mgh (Gravitational potential energy)
Ek=mgxdisplacement (if you don't have velocity?)

I would appreciate ANY help...I don't get what I'm supposed to do.

P.S. the answer in the book says it should be 31.4m/s :)
 
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You assume that the groud is zero potential: Then the initian kinetic energy is T_i =1/2mv_i^2
And the initial potential energy is 70J the 70J is all being converted to kinetic energy when it falls so make your equation and solve it:
E_{initial}= 70J+T_i = E_{final}
 
Thank you :)
 

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