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y90x

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## Homework Statement

I’m working on a problem that requires adding 3 vectors . And while I was following the book, it said to find the angle to divide the y over the x components of the resistant , and showed the angle to be -1.25 but then follow d to change to -51 .

How did it change ? The book doesn’t explain I’ll inclide a photo of the textbook so you can see what I’m talking about

Here’s the problem I’m working on just in case:

Three horizontal ropes are tied to a 30 kg mass resting on a rough surface. The coefficient of friction between the mass and the surface is 0.12. Rope A has tension 60 N directed Northwest, rope B has tension 70 N directed 20° East of South, and rope C has tension 80 N directed 35 North of West. Find the resulting acceleration of the 30 kg mass.

## Homework Equations

The component method for adding vectors

## The Attempt at a Solution

Rope A :

-60cos(45) + 60sin(45)= A

-42.426 + 42.426 = A

Rope B :

70cos(20) + -70sin(20) = B

65.778 + -23.94

Rope C:

-80cos(35) + 80sin(35) = C

-65.532 + 45.886 = C

To find the resultant magnitude :

Square root of ( all the X components added up) (-42,1800)^2 + 64.3711^2 ( all the Y components added up)

= 76.959

To find the angle :

Pheta = tan^(-1)(Y/X)

= tan^(-1) (64.3711/-42.1800)

= -56.8 Solution of the actual problem :

1.72 m/s^2 at 15.0 north of westhttps://www.physicsforums.com/attachments/215616