Hello, Thanks for requesting my help. Here is the explanation.
First note, that the person gets hurt if he stops abruptly, in case of the cushion he stops upon going through the cushion. The explanation is based on the impulse-momentum relation:
Ft = mv, where F is the average force, t is time of the impact and v is the initial velocity: From this equation we get:
F=mv/t, so you clearly see that if t is large, the F is smaller, so you conclude that once the time of the impact is long, the force is small and the persons would not get hurt.
Hope this helps
let me know if there are any questions, I'll be glad to assist.
So the t is large due to the time it takes him to go through the cushion. So the higher the cushion the greater the time and less the force. Did I get that right. thanks..
Yes, exactly! note that the product t*force stay the same as it is equal to mv, so if you can make the time t larger, then the force automatically becomes smaller, hence it would not hurt the person.