# Kinetic and Potential energy of an Aeroplane

If an aeroplane is flying horizontally at an altitude of H , and with a constant velocity of V (no air resistance) horizontally .

Is there a relationship between the potential energy of the aeroplane due to its vertical height and its kinetic energy due to its horizontal velocity?

Is it correct that $E_p + E_k$ is equal to the Total Mechanical Energy?

• No. A plane at one altitude can fly at any speed it wants to. – user1936752 Aug 22 '15 at 13:50

Just to clarify the comment above a little.

You can treat the velocity of your plane, neglecting air resistance, as completely independent of it's height, if you have studied vectors you may know how this can be drawn out on a graph.

The plane has a potential energy, mgh (mass by g by height) and this potential energy does not depend in any way on how fast it is flying in a horizontal direction.

It's kinetic energy, at a constant velocity, is the same at every height it flies at, again ignoring the air resistance, so it's kinetic energy is independent of it's height.

Kinetic energy is (1/2)mv$^2$ and potential energy is mgh. The total energy of the plane is the sum of those two sources of energy.

Have a look at this link Total Mechanical Energy and scroll down to the last section of the page to their definition of Total Mechanical Energy (TME) and their example.

• thanks. Correct me if im wrong, but is the kinetic energy then mv^2/2 and the potential energy mgh, and the total mechanical energy the sum of those? or is the total mechanical energy = mgh, since the vertical speed = 0 at height h? – Carefullcars Aug 22 '15 at 14:36