Superman's work on the asteroid is calculated with the formula W = F × d × cos(θ). The negative result indicates that Superman's work is done against the asteroid's motion, resulting in -5.15 × 10^4 J.
The problem requires us to calculate the work done by Superman on the asteroid while pushing it with a force at an angle. The work done by a force when the force and displacement are at an angle is given by W = F × d × cos(θ), where W is the work, F is the force, d is the displacement, and θ is the angle between the force and the displacement vector.
In this case, the force is at a 61.0° angle above the horizon, but the asteroid moves vertically downward, which means the angle between the force and the direction of movement is actually 180 - 61.0 = 119°. Thus, W = 361 N × 163 m × cos(119°). The cosine of 119° is negative, signaling that the work done is in the direction opposite to the force applied by Superman. Upon calculation, this results in the work done by Superman being negative, as this work is done against the direction of displacement. Using the cosine of 119° which is approximately -0.8572, the work is W = 361 N × 163 m × (-0.8572) = -5.15 × 10^4 J. Therefore, the correct answer is D. -5.15× 10^4 J.