Minimizing a vector in a triangle

In summary, the problem is to determine the magnitudes of forces F1 and F2 and the angle at which rope two pulls in order to minimize the work required by rope two when towing a truck. The resultant force should be 950N along the positive x axis, with F1 acting at 20 degrees from the x axis. The book suggests an angle of -70 degrees for rope two, but it is unclear without a diagram.
  • #1
Shaybay92
124
0

Homework Statement



A truck is to be towed using two ropes. If the resultant force is to be 950N, directed along the positive x axis, determine the magnitudes of forces F1 and F2 acting on each rope and the angle at which rope two pulls to ensure that the magnitude of F2 is a minimum. F1 acts at 20 degrees from the x axis.

The Attempt at a Solution



I assumed that to minimize the work required by rope two, it would be -90degrees angle (so it is only required to pull the truck back in line). However, the book says -70degrees?
 
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  • #2
Hi Shaybay92! :smile:

(have a degree: º :wink:)
Shaybay92 said:
I assumed that to minimize the work required by rope two, it would be -90degrees angle (so it is only required to pull the truck back in line). However, the book says -70degrees?

Sorry, no idea what you mean. :confused:

Anyway, just draw a vector triangle …

you know the direction and length of one side, and you know the direction of the second side …

what is the shortest the third side can be? :smile:​
 
  • #3
I'm assuming based on the wording that there's a diagram that goes with this? It's kinda hard to solve a geometry problem if there's supposed to be a picture with it.
 

FAQ: Minimizing a vector in a triangle

What is a vector in a triangle?

A vector in a triangle is a line segment that represents both magnitude and direction within the triangle. It is typically represented by an arrow pointing to its direction and labeled with its magnitude.

How do you minimize a vector in a triangle?

To minimize a vector in a triangle, you need to find the shortest distance between the origin (starting point) and the tip of the vector (end point). This can be done by finding the magnitude of the vector and then finding the direction of the vector using trigonometric functions.

Why is it important to minimize a vector in a triangle?

Minimizing a vector in a triangle is important because it allows us to find the shortest distance between two points in a given direction. This can be useful in various practical applications, such as navigation and optimization problems.

What are the steps to minimize a vector in a triangle?

The steps to minimize a vector in a triangle are as follows:1. Find the magnitude of the vector using the Pythagorean theorem.2. Use trigonometric functions (such as sine, cosine, and tangent) to find the direction of the vector.3. Use the direction and magnitude of the vector to find the shortest distance between the origin and the tip of the vector.

Can a vector in a triangle be minimized to zero?

Yes, it is possible for a vector in a triangle to be minimized to zero. This means that the origin and the tip of the vector are the same point, resulting in a vector with no magnitude and direction. In such cases, the vector is considered to be "trivial" and has no practical use.

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