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.

W =
−mgh

For a conservative force, how does the work done by the force compare to the change in potential energy associated with the force?

a)   W = m g h , b)     W / U = 1

Explanation:

a) work is defined by

        W = F. dy

in this case the force of gravity goes down and the displacement of the particle is down, so the two are parallel and the scalar product is reduced to the algebraic product

        W = F y

strength is the weight of the body

         F = m g

        W = m g h

where h is the distance the body descends

b) the only force acting on the body is the weight of the work and we calculated them in part a, the potential energy is

     U = m g h

to compare the two magnitudes of let's find their relationship

    W / U = mgh / mgh

    W / U = 1

it about 600 mph from what i calculated

0.55x745.7j and a calculator