A boy trying to understand gravity holds a ball above the earth and lets it fall. With aspirations of being a rocket scientist, he wonders how fast the ball would fall on another planetary bodies.

What is known:

The ball is released from rest 4 ft above the earth.

The gravitational constant is 32.2 ft/s^{2} towards the earth.

Questions

What is the velocity of the ball when it hits the earth? If the ball is being released from rest and is to have a speed of 14 mph when it hits the earth, from what height should it be dropped?

Approach

With the acceleration given as a constant, the velocity and position equations can be found by integrating the relationships, a = dv/dt and v = dx/dt.

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