Aprojectile is fired vertically from earth's surface with an initial speed of 7.3 km/s. neglecting air drag, how far above the surface of earth will it go?

We can solve the problem by using conservation of energy. 

In fact, initially the projectile has only kinetic energy, which is given by

where m is the projectile's mass while  is its initial velocity.

At the point of maximum height, the speed of the projectile is zero, so it only has gravitational potential energy which is equal to

where g is the gravitational acceleration and h is the maximum height of the projectile.

Since the energy must be conserved, we can equalize K and U to find the value of h: