Compression question (Q. 80)

[Henreezy]

Apparently the answer to question 80 is 2.7m and you compare Ek and Strain Potential Energy, can somebody help me out?

[b^3]

When she is just about to hit the mat, but hasn't hit it yet, she is travelling at 12 m/s. So her kinetic energy at this stage is
K_e=1/2 mv². Once she hits the mat, this kinetic energy will be transformed into spring potential energy in the mat. Once she comes to rest, then all the energy should have been transferred.
That is
1/2mv²=1/2kx²
So we need a value of k, looking at the graph I'm going to pick the point (2.5,3000).
So we have k=3000/2.5=1200 Nm^-1
That means that
1/2mv²=1/2kx²
x =sqrt(mv²/k)
  =sqrt(60x12²/1200)
  =2.68 m
i.e. =2.7  m

Does that help? If you still need more understanding help don't be afraid to ask

EDIT: Latex is still broken...

[Henreezy]

Alright, thanks a bunch bcubed!! I hadn't realised the gradient was equal to the spring constant, I was pretty bad at this part of year 11 physics .