Problem 3: A body of mass 2.0 kg is dropped from a rest position 5.0 m above the ground. What is its velocity at height of 3.0 m above the ground?

Solution

At the maximum height, the body has a certain amount of potential energy, mgh. As it falls down, the potential energy is converted to kinetic energy until it is totally converted into kinetic energy at the lowest point. However, on the way down, the energy possessed by the body is partly potential and partly kinetic, depending on the height from the lowest point. So, at a height of 3.0 m, it possesses P.E less than at the height of 5.0 m and the difference in potential energies is equal to the gain in K.E. Therefore, we find the K.E and the velocity will be calculated from that.

Given, state 1                    Mass of the body = 2.0 kg,           Height, h = 5.0 m

State 2                                  Mass of the body = 2.0 kg,           Height, h₂ = 3.0 m

Required                             Velocity 3 m above the ground.

Now,                                     K.E = mgh – mgh₂

Put the values,    ½ mv² =(2 × 9.8 × 5)- (2 × 9.8 × 3)    OR     ½ × 2v² = 98 – 58.8 = 39.2

OR         v² = 39.2               OR          v = √39.2              OR          v = 6.3 ms^-1 (Answer)