Originally Posted by **MBW** I think the intention is that spring 1 is initially pulled down (storing energy) then released, transferring energy to the mass and propelling it up until it hits spring 2, compressing spring 2 with its residual energy.
I will leave the maths to someone else (like ChipP perhaps). |

I think your interpretation of the problem is probably correct - the block gets shot upward by spring 1, collides with spring 2, and compresses spring 2 by precisely 2 meters.

We can use energy principles on this. When you compress spring 1 by 5m it develops potential energy that must be enough to shoot the block upwards and compress spring 2 by 2 meters. Thr ePE induced in spring 1 is:

PE_1 = (1/2) K_1 (5m)^2

which must equal the PE gained in rising up through the Earth's gravitational field a distance of 41 meters plus the initial 5 meters plus the 2 meters, and must also induce PE into spring 2 of (1/2)K_2 (2m)^2. So:

PE_1 = mgh + PE_2, or:

(1/2) K_1 x^2 = mg(5m + 41m + 2m) + (1/2) K_2(2m^2)

Now solve for m.