Question

8.) Two forces with magnitudes of 45 pounds and 62 pounds are applied to an object. The magnitude of the resultant is 100 pounds. Find the measurement of the angle between the resultant vector and the vector of the 45 pound force to the nearest whole degree. 9.) Two forces with magnitudes of 200 pounds and 340 pounds are applied to an object. The magnitude of the resultant is 150 pounds. Find the measurement of the angle between the resultant vector and the vector of the 200 pound force to the nearest whole degree.

Answer 1

8) For two vectors A and B inclined at an angle $\theta$ resultant vector R is usually given by the equation

R = VA2+B2+2AB cos 8

Putting the values given,

100 = V452 + 622 + 2 x 45 x 62 cos e

or, 100% = 45% +622 + 2 x 45 x 62 cos 0

100 – 45 – 622 or, cos 6 = = 0.7403 2 x 45 x 62

or, 0 = 42.24

If $\phi$ be the angle between R and A then we must have

tan = B sind A+B cose

or, tan 62 sin 42.24 = 45 +62 cos 42.24° +62 cos 42.240 = 0.4585

or, o = 24.6325

This is the angle between the resultant vector and 45 pound force.