A gymnast of mass 65 kg bounces vertically on a trampoline so that she approaches and leaves the trampoline with a speed of 10 m/s and
contact time of 0.9 s. Calculate (1) her change of momentum (ii) the
average resultant force exerted on her while in contact with the
trampoline​

Change in momentum:

Average resultant force: approximately .

Explanation:

Consider an object of mass travelling at velocity . The momentum of this object would be .

Momentum is a vector. The direction of an object's momentum is the same as the direction of its velocity.

Initial velocity of this gymnast: . This value is negative because the gymnast was initially travelling downwards.

Hence, the initial momentum of this gymnast would be:

.

Velocity of this gymnast after leaving the trampoline: .

Hence, the momentum of this gymnast when leaving the trampoline would be:

.

Change in momentum:

.

By Newton's Second Law of motion, if the momentum of an object changed by over time , the average net force on that object would be:

.

For this gymnast:

.