A 1.20-kg ball is hanging from the end of a rope.The rope hangs at an angle 25.0° from the vertical when a 15.0 m/s horizontal wind is blowing.If the wind's force on the rope is negligible,what drag force does the wind exert on the ball?
A) 32.3 N
B) 24.1 N
C) 3.68 N
D) 5.48 N
E) 11.8 N

Question

Quizplus · Accepted Answer

The drag force exerted by the wind on the ball can be found by analyzing the forces acting on the ball. The tension in the rope has a vertical component that balances the weight of the ball and a horizontal component that equals the drag force of the wind. The weight of the ball is $mg = 1.20 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 11.76 \, \text{N}$. Since the rope makes an angle of 25.0° with the vertical, the horizontal component (drag force) can be found using trigonometry: $\tan(25.0°) = \frac{\text{Drag Force}}{11.76 \, \text{N}}$. Solving for the drag force gives approximately 5.48 N.

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