I got this problem as part of a long homework packet, was able to figure out all the problems but the last 3, so here is one of them, but i dont have a book. I really have no idea on how to approach this problem, so i was hoping someone could lead me through it and help me figure it out...

I dont really know where to start, not sure of the equation i need to find the fireman velocity and how to use the given numbers. As forthe diagram, i drew one showing 100kg of his wieght pushing down, the ropes strength which is 800N while hes getting lowered. So what now? Please help me through this problem, i dont have a book and have looked online for formulas and similar problems but cant find any.

So far i got...
the fireman is accelerating such that ma=mg-800N
i think i have to find a, but i dont know how to, can you guys help me find it?
after i find a, i can find v by doing d=v^2(2a) where D is 10m, but i dont know how to find a so thats olding be back.
after i find v, the aveerage force of impact is mv^2/2=F*d, where d=20cm
So i guess my questions are how do i find acceleration and am i right with what my other work is? Im hoping someone can help so i can finally finish this and get some sleep. :zzz:

100kg weight is about 1000N (Weight=mg, I used g =10 because i'm tired too.) 1000 down, and 800 up is the max, that's a net of 200 down, right? F_net=ma, per Newton2. 200 = 100a. a=2. Examine the forces and write the right equation. Now let's get some zzzz's.....

It looks like you are able to use energy methods, that's probably all you need to solve this problem.

If the fireman were in free fall, then all of the potential energy would be converted to kinetic energy, by the conservation law, so that

K_final - U_Start = 0

However, there is an external force here, which is the rope. The rope is doing work, it is actually bleeding energy out of the system that would have gone into kinetic energy. So the system is losing energy. So...

K_final - U_Start = ????

If you can figure that out, then you can solve for the velocity.

Speaking of sleep.. What a good idea. Hope this is enough to help you solve it now.