- Sam pulls with 200 Newtons of force at 60°
- Alex pulls with 120 Newtons of force at 45° as shown
What is the combined force, and its direction?
Let us add the two vectors head to tail:
First convert from polar to Cartesian (to 2 decimals):
Sam's Vector:
x = r × cos( θ ) = 200 × cos(60°) = 200 × 0.5 = 100
y = r × sin( θ ) = 200 × sin(60°) = 200 × 0.8660 = 173.21
Alex's Vector:
x = r × cos( θ ) = 120 × cos(−45°) = 120 × 0.7071 = 84.85
y = r × sin( θ ) = 120 × sin(−45°) = 120 × -0.7071 = −84.85
Add them:
(100, 173.21) + (84.85, −84.85) = (184.85, 88.36)
That answer is valid, but let's convert back to polar as the question was in polar:
r = √ ( x2 + y2 ) = √ ( 184.852 + 88.362 ) = 204.88
θ = tan-1 ( y / x ) = tan-1 ( 88.36 / 184.85 ) = 25.5°
