Help with this problem from kaplan?

[m25]

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I've uploaded the question below. How do we know that net did the same amount of work on both of them because Tom and Mary landed on the net at the same time? I thought Tom had more energy because he had the higher potential energy. I am not able to follow with their reasoning at all...

 

[Cawolf]

That's a tricky question.

I think they are trying to explain that both people compress the spring together so the sum of their kinetic energies is converted into the potential energy of the spring. This spring then exerts an equal force on each person because it is simultaneous. The work the spring does on each person is converted into kinetic and then potential energy. By conservation of energy they will each go back to the height they started at (ignoring all the aspects in reality that would drain energy from these interactions).

 

[m25]

That's a tricky question.

I think they are trying to explain that both people compress the spring together so the sum of their kinetic energies is converted into the potential energy of the spring. This spring then exerts an equal force on each person because it is simultaneous. The work the spring does on each person is converted into kinetic and then potential energy. By conservation of energy they will each go back to the height they started at (ignoring all the aspects in reality that would drain energy from these interactions).

>This spring then exerts an equal force on each person because it is simultaneous.

But according to choice C, which must be true, Tom experiences more force than Mary(which I'm guessing is due to him having higher change in momentum MV=Ft).

I'm still very confused but the overall point of this question is that all the energy is conserved, so Tom and Mary will both end up where they started, ie the same height?
So that means both Tom and Mary's energy is conserved all throughout, and as each of their energy goes from gravitational to kinetic to elastic to kinetic to potential, Tom's energy will always be higher because he starts out with higher potential energy(due to his greater mass). So then why is the explanation saying that the "net does the same amount of work on both of them"?

 

[Cawolf]

I agree that the overall point is conservation of energy and energy "transformation".

I believe that choice C is referring to the initial collision with the net, not the rebound and upwards force after it is compressed.

If they each receive an equal force due to simultaneous "launch" upwards then they will both reach the same height they started at, but the lighter person will get there faster due to a greater acceleration.

The work is equal on each because they both experience the same force over the same distance.

These are mostly rationalizations after reading the answer. As a test taking strategy I would've eliminated all except A and B, then checked the math and picked A.