Solving Physics Problem with Angles and Trigonometry

[Angetaire]

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 F₁ and F₂ respectively.
- There are no net force in the x-direction, so F(total x) = 0.
- F_{(total y)} = F₁ + F₂ - mg = 0 (initially). Rearranging gives g = [F₁+F₂]/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 = 1/2gt²
- Insert g gives H = [F₁+F₂]t²]/2m
- From this equation I gathered that H is proportional to F₁ and F₂. So as the height increases, F₁ and F₂ 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 F₁. F₁= sqrt(h²+(d/2)²).
- So the F_{(total y)} at height h = 2sqrt(h²+(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.

 

[BvU]

Hello @Angetaire ,

$\qquad$ !​

F(total y) = F1 + F2 - mg = 0

In the line just above, you have written that $F_1 + F_2 = 0$ (equal and opposite) !

 

[BvU]

Anyway: make a sketch for the case the ropes are at 45 degrees -- you see that F1 and F2 each have a y-component that is not equal to the magnitude ...

$\$

 

[BvU]

H = 1/2gt²

There is no free fall in this exercise ! Neither downward (unless one of the 'friends' let's go or the rope breaks), not upwards !

$\$

 

[BvU]

Sorry I'm self-learning with no tutor

No need to apologise ! On the contrary: kudos! PF is a good place to solicit comments, so keep

do more problems