Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.
-
A.
39.45° -
B.
73.40° -
C.
75.34° -
D.
106.60°
Correct Answer: Option B
Explanation
(F_{1} = 7i + 0j)
(F_{2} = (4costheta)i + (4sintheta)j)
(9 = sqrt{(7 + 4costheta)^{2} + (4sintheta)^{2}})
(9^{2} = (7 + 4costheta)^{2} + (4sintheta)^{2} implies 81 = 49 + 56costheta + 16cos^{2}theta + 16sin^{2}theta)
(81 = 49 + 56costheta + 16(cos^{2}theta + sin^{2}theta))
Recall, (cos^{2}theta + sin^{2}theta = 1)
(81 = 49 + 56costheta + 16 implies 81 – 49 -16 = 56costheta)
(16 = 56costheta implies costheta = frac{16}{56} = 0.2857)
(theta = cos^{-1} 0.2857 = 73.40°)