Kinetic energy and Gravitational Potential Energy

[Sabeshan Ratneswaran]

Hi Guys,When we are finding the wasted energy when something is dropped a tower, we do this: mgH-0.5mv^2
My question is, does the velocity of the kinetic energy have to be vertical component, or can it be the impact velocity when it hits the ground?

Thanks

 

[Merlin3189]

If you simply drop an object,it will fall vertically. The vertical component of its motion will be its only motion. Gravity can not give it a horizontal component. If you give it a horizontal component, you have given it some KE. This then remains constant (assuming no resistance.) Only the vertical component of velocity increases as it falls. So if you are considering gravitational potential energy, you are only interested in the vertical component of motion.
For a dropped object mgH = 0.5m(vv)²
For a thrown object 0.5m(vh)² +mgH = 0.5mv² = 0.5m(vh)² + 0.5m(vv)² which reduces to the above when you cancel the horizontal component.