"a 10 kg rock is pushed off the edge of a bridge 50 meters above the ground. what was the kinetic energy of the rock at the midway point of its fall? "

Let's call h the initial height of the rock (h=50 m, the height of the bridge).

Initially, the rock has only gravitational potential energy, which is given by

where m=10 kg is the mass of the rock while g is the gravitational acceleration. So, the total mechanical energy of the rock at this point is


At midway point of its fall, its height is , so its potential energy is

But now the rock is also moving by speed v, so it also has kinetic energy:

So the total energy at the midway point of the fall is
(1)

The mechanical energy must be conserved, so , so we can rewrite (1) and solve it to find the kinetic energy of the rock at midway point of its fall: