Solve.
-Two forces of 24 and 52 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force.
A) 57 N, 65°
B) 57 N, 75°
C) 3280 N, 65°
D) 57 N, 25°

Question

Quizplus · Accepted Answer

The magnitude of the resultant force can be found using the Pythagorean theorem since the forces act at right angles to each other: $\sqrt{24^2 + 52^2} = \sqrt{576 + 2704} = \sqrt{3280} = 57$ N. The angle $\theta$ with the smaller force (24 N) can be found using the tangent function: $\tan(\theta) = \frac{52}{24}$, which gives $\theta \approx 65^\circ$.

Solve. -Two Forces of 24 and 52 N (Newtons) Act on on an Object