A projectile is shot at some inclination to the ground. It falls at another point having R distance from the initial point on the ground. Is there any work done?
If initial velocity vector is $(u\cos A,u\sin A)$, when it hits the ground, its velocity will be $(u\cos A,-u\sin A)$. Change in vertical component of velocity is $2u\sin A$ in downward direction.
When velocity changes in direction or magnitude, a force is involved. As force is change in momentum wrt time.
Is there any work done? because as the initial total energy of the projectile and final total energy of the projectile same. Shouldn't the work done during upward motion cancel the work done in downward motion?