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Find the angle between forces of 41 pounds and 68 pounds given a magnitude of 87 pounds for the resultant force. (Hint: Write force one as a vector in the direction of the positive x-axis and force two as a vector at an angle θ with the positive x-axis.)

Respuesta :

Answer:

[tex]\theta = 76.9 degree[/tex]

Explanation:

As we know that the resultant of two vectors is given as

[tex]R = \sqrt{F_1^2 + F_2^2 + 2F_1 F_2 cos\theta[/tex]

here we know that

[tex]R = 87 Lb[/tex]

[tex]F_1 = 41 Lb[/tex]

[tex]F_2 = 68 Lb[/tex]

now we have

[tex]87 = \sqrt{41^2 + 68^2 + 2(41)(68)cos\theta[/tex]

[tex]87^2 = 6305 + 5576 cos\theta[/tex]

[tex]\theta = cos^{-1}(\frac{1264}{5576})[/tex]

[tex]\theta = 76.9 degree[/tex]

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