Adding Vectors-Calculating Magnitude and Location

[kevbos]

Homework Statement

Homework Equations

Pythagorean Theorem?

The Attempt at a Solution

I know you have to add the vectors to get the location. like (3,x) +(-5,-12), but I'm stuck from there. The last bit has no coordinates (x,0). For the first vector do I need to use Pythagorean theorem to solve for y? By adding these coordinates I would get the location, but how do I get the magnitude? Do I add 10, 4 and 16?

 

[RJLiberator]

It's kind of hard to read the image, but I'd first start off by finding the y-component of the first force.

 

[NFuller]

I'm sort of bewildered by what the question is asking. What do they mean by find a force vector and its location. Its almost as if they want you to treat the vector as both a force and a distance. The problem is it can't be. The vector can only have one set of units so its one or the other.

Am I missing something?

 

[vela]

I wonder if by asking for location, the problem is asking for the resultant force in component form.

 

[CWatters]

My guess is the problem should read..

Find the final vector magnitude and direction.

 

[CWatters]

I know you have to add the vectors to get the location. like (3,x) +(-5,-12), but I'm stuck from there.

These are force vectors not displacement vectors. You can still add them using the same methods (eg head to tail method) but you get a resultant (total) force vector not a location. The resultant force vector runs from the origin (tail of first vector) to the head of the last vector.

The last bit has no coordinates (x,0).

The 3:5 and -12:-5 are not co-ordinates. They are telling you the direction of the vector (eg the slope or gradient). For example the first vector is at an angle of Tan^-1(5/3) with respect to the horizontal.

The figure in lb is the magnitude of the force.

For the first vector do I need to use Pythagorean theorem to solve for y? By adding these coordinates I would get the location, but how do I get the magnitude? Do I add 10, 4 and 16?

For the first vector you know the magnitude (aka length) is 10 and can calculate the angle with the horizontal from the slope. You can then use trig to get the x and y components of the force.

Sorry for the minor edits I've had to make to this reply. I got interrupted.

 

[CWatters]

For example the first vector is at an angle of Tan-1(5/3) with respect to the horizontal.

Correction: The 5 is next to the hypotenuse so this is a 3-4-5 triangle and the angle is Tan^-1(4/3).