# Solving Physics Problem with Angles and Trigonometry

• Angetaire
In summary, the correct solution uses angles and trigonometry. My solution is as follows:- 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
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.

Hello @Angetaire ,
Angetaire said:
F(total y) = F1 + F2 - mg = 0
In the line just above, you have written that ##F_1 + F_2 = 0 ## (equal and opposite) !

Angetaire
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 ...

##\ ##

Angetaire
Angetaire said:
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 !

##\ ##

Angetaire
Angetaire said:
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
Angetaire said:
do more problems

Angetaire

## What is the purpose of using angles and trigonometry in solving physics problems?

Angles and trigonometry are used in physics to calculate the relationships between different forces and objects in motion. By using angles and trigonometry, we can determine the direction and magnitude of forces, as well as the distance and speed of objects.

## What are the basic trigonometric functions used in solving physics problems?

The basic trigonometric functions used in physics are sine, cosine, and tangent. These functions are used to calculate the ratios of sides in a right triangle, which are essential in solving problems involving angles and distances.

## How do I use trigonometry to solve for an unknown angle in a physics problem?

To solve for an unknown angle using trigonometry, you will need to use the inverse trigonometric functions, such as arcsine, arccosine, and arctangent. These functions will help you find the angle when given the ratios of the sides of a right triangle.

## Can I use trigonometry to solve problems involving non-right triangles?

Yes, trigonometry can also be used to solve problems involving non-right triangles. In these cases, we use the law of sines or the law of cosines, which involve using the ratios of sides and angles in a triangle to find the missing information.

## How do I know when to use angles and trigonometry in a physics problem?

Angles and trigonometry are commonly used in physics problems involving forces, motion, and projectiles. If a problem involves calculating distances, angles, or forces, it is likely that you will need to use angles and trigonometry to solve it.

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