A particle is projected in gravity with a speed `v_0`. Using W-E theorem, find the speed of the particle as the function of vertical distance y.

Explanation

Let the particle move up through a height y between points 1 and 2. The work done by gravity in shifting the particle from point 1 to 2 is
`W_(gr)=-mgy`

The change in kinetic energy is
`DeltaK=1/2m(v^2-v_0^2)`
Substituting `W=W_(gr)=-mgy` and `DeltaK=1/2m(v^2-v_0^2)` in `W-E` theorem, `W=DeltaK`, we have
`m/2(v^2-v_0^2)=-mgy`
This gives `v=sqrt(v_0^2-2gy)`