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

`\theta = 76.9 degree`

Step-by-step 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)((1264)/(5576))`

`\theta = 76.9 degree`