Physics energy question

[theonlytycrane]

This is from Kaplan MCAT Physics and Math review - problem #11 of the Work and Energy chapter.

Question: Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true?

a) Sarah will bounce higher than Josh.
b) For Josh, the change in speed from the start of the jump to contacting the net is 20 m/s.
c) Josh will experience a greater force upon impact than Sarah.
d) The energy in this event is converted from potential to kinetic to elastic to kinetic.

Choice (a) is the incorrect statement. What I'm wondering is if they will hit the ground at the same time? Josh has more potential energy than Sarah and will experience a greater change in speed from the start of the jump to contacting the net. Also, assuming that energy is conserved they will bounce back up to the same height as they originally were at. Where is the difference in mass between Josh and Sarah accounted for?

Thanks!

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[jb94mg]

They will have the same acceleration on the way down since gravity accelerates everything at the same rate (9.8 m/s^2). And yes, they'll hit the ground at the same time - it says that in the question ("they bounce back up at the same time"). You know this since they'll be accelerating at the same rate, and as a result, falling at the same speed.

Since Josh has a greater mass, both the force on the fire net from him and the equal-and-opposite force he'll receive upon impact (see answer c) with the fire net will be greater than the forces Sarah will receive and produce, which is why he'll still reach the same height despite accelerating at a lesser rate, and despite having the same acceleration when he hits the fire net.

I hope this helps you.

Relevant info:
F = ma (Newton's second law)
https://en.wikipedia.org/wiki/Gravitational_acceleration
https://van.physics.illinois.edu/qa/listing.php?id=164

This is from Kaplan MCAT Physics and Math review - problem #11 of the Work and Energy chapter.

Question: Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true?

a) Sarah will bounce higher than Josh.
b) For Josh, the change in speed from the start of the jump to contacting the net is 20 m/s.
c) Josh will experience a greater force upon impact than Sarah.
d) The energy in this event is converted from potential to kinetic to elastic to kinetic.

Choice (a) is the incorrect statement. What I'm wondering is if they will hit the ground at the same time? Josh has more potential energy than Sarah and will experience a greater change in speed from the start of the jump to contacting the net. Also, assuming that energy is conserved they will bounce back up to the same height as they originally were at. Where is the difference in mass between Josh and Sarah accounted for?

Thanks!

 

[mydogmolly]

Instead of starting a new thread I just wanted to revive this one. I came across this same problem just now, and obviously I got it wrong.

My intuition is that because of the phrasing of the question, I assumed Josh and Sarah were sharing a net, meaning their combined potential energy is transferred to total elastic potential. And from there my intuition was that they would split the elastic potential equally, meaning Josh won't bounce has high as Sarah.

I calculated to their added potential/kinetic energy as 260kJ. So if total elastic potential is 260kJ, they then both receive an effective 130kJ. Since Josh is ~300N heavier, his new max height will only be around 16m, whereas Sarah will go back up to 26m. Come to think of it, I've observed this when playing with my nephews on trampolines, where we try to land on the trampoline at the same time, and my kid nephews get tons of air whereas I almost don't bounce at all. Is that fair?

I guess my question is that generally how do two different masses on the same elastic system (net/spring/whatever) act when the total elastic potential is transferred to kinetic? Imagining a system where you have two toy cars of different masses being cocked by a spring aimed up a ramp, my intuition is that the lighter car will travel higher up the ramp.