Question

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.)

Answer 1

Answer:

$\theta = 76.9 degree$

Explanation:

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

$R = \sqrt{F_1^2 + F_2^2 + 2F_1 F_2 cos\theta$

here we know that

$R = 87 Lb$

$F_1 = 41 Lb$

$F_2 = 68 Lb$

now we have

$87 = \sqrt{41^2 + 68^2 + 2(41)(68)cos\theta$

$87^2 = 6305 + 5576 cos\theta$

$\theta = cos^{-1}(\frac{1264}{5576})$

$\theta = 76.9 degree$