What is the angle [theta] for the tug B in the given diagram?

Using this information, a ratio can be created to find the angle [theta]. The attempt at a solution involves setting up a proportion and solving for [theta]. However, this approach may not be logical and therefore, further suggestions are needed to find the correct solution.
  • #1
fs93
12
0

Homework Statement


I've got a diagram but here's the question.
Two tugs A and B pull a ship along the direction XO.
Tug A pulls the ship with a force of 30kN at an angle of 15°.
Tug B pulls the ship with a force of 18kN at an angle of [theta]

Find the angle [theta]


Homework Equations





The Attempt at a Solution


I've tried creating a ratio to find the value [theta].
30/15=18/x
x=9°

But I don't think that's right as it doesn't seem logical.

Any suggestions ? :)
 
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  • #2
Since the ship is moving along XO direction due to forces, their y components must cancel each other. Find the y-component of 30kN and 18 kN and equate them.
 
Last edited:
  • #3
rl.bhat said:
Sine the ship is moving along XO direction due to forces, their y components must cancel each other. Find the y-component of 30kN and 18 kN and equate them.

Their y components as in horizontal components? And by equate them, what do you mean?
 
  • #4
fs93 said:
Their y components as in horizontal components? And by equate them, what do you mean?
In the given problem if XO represents the x-axis, then the vertical components must get canceled out.
 

1. What is a resolution vector?

A resolution vector is a mathematical concept used in vector analysis to represent a vector in terms of its components along different axes. It is used to simplify vector calculations and is particularly useful in solving problems involving multiple vectors.

2. How do you calculate the resolution vector?

The resolution vector is calculated by using trigonometric functions to determine the components of the vector in the x and y direction. The formula for calculating the x component is given by Rx = R * cosθ, and the formula for calculating the y component is given by Ry = R * sinθ, where R is the magnitude of the vector and θ is the angle it makes with the x-axis.

3. What is the purpose of using resolution vectors?

The purpose of using resolution vectors is to simplify vector calculations. By breaking down a vector into its components, it becomes easier to find the resultant vector, determine the direction and magnitude of the original vector, and solve problems involving multiple vectors.

4. Can resolution vectors be negative?

Yes, resolution vectors can be negative. The sign of a resolution vector depends on the direction in which it is pointing. If the vector is pointing in the positive direction, its component will be positive, and if it is pointing in the negative direction, its component will be negative.

5. Are resolution vectors only used in two dimensions?

No, resolution vectors can be used in any number of dimensions. While the most common use of resolution vectors is in two dimensions, they can also be extended to three or more dimensions by using trigonometric functions to determine the components of the vector in each direction.

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