Question

Two forces, one of 45 pounds and the other 50 pounds, act on the same object. The angle between the forces is 33°. Find the magnitude of the resultant vector. Pls help :( cant afford to fail

Answer 1

The magnitude of the resultant force is: 27.40 pounds

Explanation:

Given

`F_1 = 45`

`F_2 = 50`

`\theta = 33`

Required

The magnitude of the resultant vector

To do this, we apply cosine formula

`R^2 = F_1^2 + F_2^2 - 2 * F_1 * F_2 * \cos(\theta)`

This gives:

`R^2 = 45^2 + 50^2 - 2 * 45 * 50 * \cos(33)`

`R^2 = 2025+ 2500 - 4500* 0.8387`

`R^2 = 2025+ 2500 - 3774.15`

`R^2 = 750.85`

Take square roots of both sides

`R = \sqrt{750.85\\`

`R = 27.40`