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# M1 help watch

1. Each of two forces has magnitude X N, and the resultant of the two forces has magnitude 12N. When the magnitude of one of the forces is increased by 70% the magnitude of the resultant of the two forces becomes 21N. Find X and the angle between the two forces

I know in the second one. One must use 1.7x.

However, still not sure about how to go about it. Help would be appreciated.
2. Are you provided with a diagram?
3. Nope.
4. (Original post by Deep456)
Nope.
It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
5. (Original post by steve2005)
It's a puzzle. Have you typed the question EXACTLY as printed. If not can you give the exact wording?
Well it's from a friend of mine and he says he gave it exactly as it is written.

We have both establised:

12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

Now how to solve?
6. I think these are the diagrams. The angle theta is NOT the required angle but when you know this it is easy to get the required angle.

7. (Original post by Deep456)
Well it's from a friend of mine and he says he gave it exactly as it is written.

We have both establised:

12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

Now how to solve?
Make the subject of both equations and then solve for X then find angle.
8. (Original post by Deep456)
Well it's from a friend of mine and he says he gave it exactly as it is written.

We have both establised:

12² = X² + X² + 2XXcos(theta) = 2X²(1+2cos(theta))

21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

Now how to solve?
21² = X² + (1.7X)² + 2X(1.7X)cos(theta) = 2.89X² + 3.4X²cos(theta)

The bold should be 3.89X²
9. (Original post by Deep456)
Now how to solve?
I'm inclined to make the entire "x^2Cos(theta)" term the subject of each, equate the two, and solve the quadratic for "x".

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