A force of 890 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of 13.0°. What is the weight of the boat and its trailer? Round to the nearest pound.
A) 3956 pounds
B) 913 pounds
C) 3855 pounds
D) no solution

Question

Quizplus · Accepted Answer

The weight of the boat and its trailer can be found using the formula for the component of weight parallel to the incline, which is $ W \sin(\theta) = F $, where $ W $ is the weight, $ \theta $ is the angle of incline, and $ F $ is the force required to pull the object. Rearranging for $ W $, we get $ W = \frac{F}{\sin(\theta)} $. Substituting $ F = 890 $ pounds and $ \theta = 13.0^\circ $, we find $ W = \frac{890}{\sin(13.0^\circ)} \approx 3956 $ pounds, rounding to the nearest pound.

A Force of 890 Pounds Is Needed to Pull a Speedboat