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Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Vectors and horses

Hello amicable MIF members,
I've tried to comprehend these vector questions but they've been making no sense whatsoever. Take a look.

1. A horse is pulling in a large rock with a force magnitude of 600 lb in the direction of 47 degrees. I can pull the rock with a force magnitude of 225 lb, but I need to move in the direction of 51 degrees. In what direction should I pull the rock.
My (solution?):
Note that all degrees are referring to BEARINGS(My teacher told me this.).. so the components are..
HORSE: 600cos(43 d), 600 sin(43 d) (because 90 - 47 = 43 deg)
HUMAN:225cos(x), 225sin(x)
So.. let's use atan(or inv tan)

tan^-1((600sin(43 d) + 225sin(x))/(600cos(43 d) + 225cos(x))) =  53 deg
(because tan is o/a.. vert/horizontal)
WolframAlpha provides me with an answer of 115 degrees.. which doesn't really make sense.. because if the human pulled that way, then wouldn't the 47 deg decrease?
DIAGRAM:

2. Suppose v = <-2, 5> is decomposed into vectors u and w, such that u and w are orthogonal to each other, and u is parallel to vector <3, -1>, and u + w = v. find u and w.
I think this involves projection, but how do you make it parallel to <3, -1>?

Thank you, benevolent MIF members.

---

The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

alter ego

Member

Registered: 2012-03-30

Posts: 29

Re: Vectors and horses

Hi Mathegocart,

I haven't got access to my geometry program at the moment but 115 looks ok with a rough sketch. The parallelogram of forces has a long side for the horse so the human has to have a southward component to change the angle to 51.

For the second one the orthogonal vector will have the form (1 , 3).  Form an equation using lambda and mu

(-2 , 5) = lambda(3 , -1) + mu(1 , 3) and solve for the unknowns.

Bob