Vector physics help!

Question

Suppose a body has a force of 10 pounds acting on it to the right, 25 pounds acting on it -135° from the horizontal, and 5 pounds acting on it directed 150° from the horizontal. What single force is the resultant force acting on the body?

Answer 1

In the horizontal direction you have:

 

[10 + 25cos(-135º) + 5cos(150º)] pounds = -12.01 pounds

 

In the vertical direction you have:

 

[25sin(-135º) + 5sin(150º)] pounds = -15.18 pounds

 

Magnitude of resultant force:

 

√[(-12.01)² + (-15.18)²] pounds = 19.36 pounds

 

θ = tan^-1(-15.18 / -12.01) = 51.65º → below the negative x-axis

 

The resultant force has a magnitude of 19.36 pounds and points 51.65 degrees below the negative x-axis