Question

A mass M,initially at rest, is dropped from a height H. State the relation between the kinetic energy of the falling object and its subsequent height

Answer 1

Let the mass M be dropped from the height at rest (i.e., u = 0) and let it attain a velocity V on being at a height X, so that the distance travelled by the mass during this time is H - X.

For a freely falling body, acceleration is nothing but g. Then, we have the second kinematic equation, $\quad$

v² = u² + 2as

V² = 2g(H - X)

Then the kinetic energy of the mass is,

K = MV² / 2

K = Mg(H - X)

The equation implies the kinetic energy of the mass increases as its height from ground reduces to zero, i.e., as X ↑, then K ↓.