Answer:
e. the air mattress exerts the same impulse, but a smaller net avg force, on the high-jumper than hard-ground.
Explanation:
This is according to the Newton's second law and energy conservation that the force exerted by the hard-ground is more than the force exerted by the mattress.
The hard ground stops the moving mass by its sudden reaction in the opposite direction of impact force whereas the mattress takes a longer time to stop the motion of same mass in a longer time leading to lesser average reaction force.
<u>Mathematical expression for the Newton's second law of motion is given as:</u>
............................................(1)
where:
dp = change in momentum
dt = time taken to change the momentum
We know, momentum:
Now, equation (1) becomes:
<em>∵mass is constant at speeds v << c (speed of light)</em>
and, 
where: a = acceleration
also
so, more the time, lesser the force.
<em>& </em><u><em>Impulse:</em></u>
∵Initial velocity and final velocity(=0), of a certain mass is same irrespective of the stopping method.
So, the impulse in both the cases will be same.
