An object is projected upward from the surface of the earth with an initial speed of 3.7 km/s. find the maximum height it reaches.

The kinetic energy of the object just after it starts its motion from the Earth surface is

where m is the object mass and its initial speed.
When it reaches its maximum height, the object speed is zero and all its kinetic energy converted into gravitational potential energy, which is

where and h is the maximum height reached by the object.

Since the energy of the object must be conserved, K=U, therefore we can write

and we can solve to find h, the maximum height: