Answered

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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

Sagot :

MrRoyal

Answer:

The magnitude of the resultant force is: 27.40 pounds

Step-by-step explanation:

Given

[tex]F_1 = 45[/tex]

[tex]F_2 = 50[/tex]

[tex]\theta = 33[/tex]

Required

The magnitude of the resultant vector

To do this, we apply cosine formula

[tex]R^2 = F_1^2 + F_2^2 - 2 * F_1 * F_2 * \cos(\theta)[/tex]

This gives:

[tex]R^2 = 45^2 + 50^2 - 2 * 45 * 50 * \cos(33)[/tex]

[tex]R^2 = 2025+ 2500 - 4500* 0.8387[/tex]

[tex]R^2 = 2025+ 2500 - 3774.15[/tex]

[tex]R^2 = 750.85[/tex]

Take square roots of both sides

[tex]R = \sqrt{750.85\\[/tex]

[tex]R = 27.40[/tex]

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