A small sphere of mass m is launched horizontally over a body of water from a he

Question

A small sphere of mass m is launched horizontally over a body of water from a height h above the water and with a launch speed v0. Determine expressions for the following in terms of m, v0, h, and g. Air resistance is negligibly small.

(a) W is the amount work done by the force of gravity on the projectile during its flight.

(b) KE is the change in kinetic energy KE of the projectile from the time it was fired until it hits the water.

(c) KEf is the final kinetic energy KEf of the projectile as it hits the water.

Explanation / Answer

(a) For a conservative force, the work done by the force acting over a distance is the negative of the change in potential energy associated with that force. This allows us to write

Wg = PEg = (mgy) = mg(h) = mgh.

(b) According to the workenergy theorem, the net work done on an object is equal to the change in its kinetic energy. This allows us to write

K = Wnet = Wg = mgh.

(c) Since energy is conserved,

K = PE,

or Kf Ki = (mgh)

or Kf = Ki + mgh = mv02/2 + mgh

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