An object of mass m is projected from the ground with initial speed `v_(0)` Find the speed at height h.

Explanation

Since the gravitational force is conservative, the total energy is conserved throughout the motion.

Final values of potential energy, kinetic energy and total energy are measured at the height h.
By law of conservation of energy, the initial and final total energies are the same.
`1/2mv_(0)^(2)=1/2mv^(2)+mgh`
`v_(0)^(2)=v^(2)+2gh , v=sqrt(v_(0)^(2)-2gh)`