Vectors Help - Word Problem?
A blimp is held in place with 2 ropes. Wind is creating a force of 300N on a bearing of 280 degrees, and one of the ropes is exerting a force of 250N on a bearing of 170 degrees. What force is being exerted by the other rope?
- PopeLv 74 weeks ago
This has been edited and corrected.
Let w be the wind vector, and let u and v be the tension vectors. Break them up into components.
w = 300sin(280°)i + 300cos(280°)j
u = 250sin(170°)i + 250cos(170°)j
u + v = -w
v = -w - u
v = -300sin(280°)i - 250sin(170°)i - 300cos(280°)j - 250cos(170°)j
v ≈ 252.0303i + 194.1075j
Both components at positive, which places it in the northeast quadrant.
r ≈ √(252.0303² + 194.10753²) ≈ 318.1 N
θ ≈ tan⁻¹(252.0303 / 194.1075) ≈ 52.4°
The missing tension vector is about 318.1 N, azimuth 52.4°.