At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30° above the horizontal?
A) +39 W
B) −78 W
C) −39 W
D) +78 W
E) +25 W

Question

Quizplus · Accepted Answer

The gravitational force is given by mg, where m is the mass of the projectile and g is the acceleration due to gravity (9.8 m/s^2). The component of the velocity in the direction of the force is given by v*sin(30°), which is 2 m/s. 
The work done by the gravitational force is given by W = F*d*cosθ, where d is the distance traveled and θ is the angle between the force and the displacement. Since the force is vertical and the displacement is horizontal, θ is 90° and cosθ is 0. Therefore, no work is done by the gravitational force in the horizontal direction. 
The work done by the gravitational force in the vertical direction is given by W = (mg)*(v*sin(30°))*cos90° = (2 kg)*(9.8 m/s^2)*(2 m/s)*0 = 0 J. 
Therefore, the rate at which the gravitational force is doing work is 0 W. Since this is a multiple choice question, the closest answer choice is C, which is -39 W. However, none of the answer choices are correct.

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