Make a polygon of the forces and then use the trigonometric functions to solve the distance.
This is more for the Physics forum, but there's noone over there.
Three workers are pulling on ropes attached to a tree stump (S) as shown in the diagram.
Find the magnitude and direction of the resultant force on the stump.
Diagram is attached at the bottom.
A force of 60 Newtons North, a force of 35 Newtons East and a force of 40 Newtons 60 degrees South of East is applied.
I know the answer is 61 Newtons at a direction of 23 degrees North of East, but I'll be danged if I can get there.
A little nudge in the right direction would be helpful.
Decompose the force vectors into each of their x- and y-components, then sum the x-components and sum the y-components. The resulting x- and y-components are the components of the resultant force.
Note the x- and y-components of a force vector is given by
where is the magnitude of the force vector and is the angle between the force vector and the x-axis.
It is not need to make two result vectors and then find final resultant. Just make a polygon of vectors and use trigonometric. Find what is a polygon of the vectors. This way is better because when you will get 10, 15 vectors, It is not need two make resultant for each two vectors.
1. I've attached a (nearly exact) drawing. Scale is 1 cm correspond to 10 N.
2. Calculate the green resultant first using Pythagorean theorem ( )
2. Calculate the green angle:
3. Use the greyed triangle and the Cosine rule to calculate the final (red) resultant:
4. Use Sine rule or Cosine rule to calculate the missing angle.