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- Homework Statement
- A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys. Show that the force (assumed equal for both the friends) exerted by each friend on the rope increases as the man moves up. Find the force when the man is at a depth h.

- Relevant Equations
- None

The correct solution uses angles and trigonometry. My solution is as following:

- Suppose the forces exerted by friends 1 and 2 are F

_{1}and F

_{2}respectively.

- There are no net force in the x-direction, so F(total x) = 0.

- F

_{(total y) }= F

_{1}+ F

_{2}- mg = 0 (initially). Rearranging gives g = [F

_{1}+F

_{2}]/m

- Initial velocity = 0, I've chosen the origin of my co-ordinate system to be at the initial y-position of the person being pulled up so initial position is (0,0). So H = 1/2gt

^{2}

- Insert g gives H = [F

_{1}+F

_{2}]t

^{2}]/2m

- From this equation I gathered that H is proportional to F

_{1}and F

_{2}. So as the height increases, F

_{1}and F

_{2}should increase as well (since they're equal). I made an assumption here that the rescue must happen within a limited time frame so greater height must be achieved with greater forces.

- Since the taut ropes make a right-angled triangle with the lip of the ditch, I take the base of the triangle on one side to be d/2, the height h, and the hypothenuse F

_{1}. F

_{1}= sqrt(h

^{2}+(d/2)

^{2}).

- So the F

_{(total y)}at height h = 2sqrt(h

^{2}+(d/2)

^{2})-mg

Is this a valid alternative solution to this problem?

PS: Sorry I'm self-learning with no tutor to help me find out. I'm learning through "Concepts of Physics" Vol 1 by H.C Verma because of it's conciseness (English second language), but there are a lot of non-worked out solutions with a single line of answer. I find myself making a lot of mistakes like this, doing something different from the correct solutions and often not knowing where to start with the more abstractly worded ones (though it's getting better as I do more problems). I attribute it to lack of grasp on material and general inexperience with solving physics problems that don't involve number-chugging. If anyone has tips on how to be a better problem-solver please share.