A body is acted upon by two forces (F_{1} = (5 N, 060°)) and (F_{2} = (10 N, 180°)). Find the magnitude of the resultant force.
-
A.
18.75 N -
B.
15.75 N -
C.
9.50 N -
D.
8.66 N
Correct Answer: Option D
Explanation
(F_{1} = (5 N, 060°) = 5 cos 60 i + 5 sin 60 j = 2.5 i + frac{5sqrt{3}}{2}j)
(F_{2} = (10 N, 180°) = 10 cos 180 i + 10 sin 180 j = -10i)
(R = F_{1} + F_{2} = -7.5 i + frac{5sqrt{3}}{2}j)
(|R| = sqrt{(-7.5)^{2} + (frac{5sqrt{3}}{2})^{2}})
= (sqrt{56.25 + 18.75} = sqrt{75})
= 8.66 N