Solve.
-Two forces of 50 and 80 N (newtons) act on an object. The angle between the forces is 42°. Find the magnitude of the resultant and the angle that it makes with the smaller force.
A) 123 N, 26°
B) 9 N, 26°
C) 121 N, 31°
D) 122 N, 26°

Question

Quizplus · Accepted Answer

The magnitude of the resultant force can be found using the law of cosines: $R = \sqrt{50^2 + 80^2 - 2(50)(80)\cos(42°)}$, which approximates to 122 N. The angle $\theta$ with the smaller force can be found using the law of sines: $\sin(\theta) = \frac{80\sin(42°)}{R}$, leading to $\theta \approx 26°$.

Solve. -Two Forces of 50 and 80 N (Newtons) Act on on an Object