where E is the energy absorbed by the surface, F is the force that the surface exerts on the athlete to stop him or her,
Note 2) The kinetic energy is also partly absorbed by the body, but not not significantly for a soft surface.
It reduces the impact force on the athlete so that he/she is not injured.
Equation for Newton's second law of motion:
For a given athlete falling from the bar they've just vaulted over to the ground the impulse is some finite value. The only variables that can be altered are the impact force and the time of collision.
From the above equation impact force and time of collision are inversely proportional.
So if the time of collision is small the impact force will be large ⇒ the athlete will be injured! However if the time of collision is large the impact force will be small ⇒ athlete is not injured.
The cushion the athlete lands on increases the time of the collision so that the impact force is reduced to the point that it will not injure the athlete.