You are riding a sled across frictionless ice. It has been given an initial push and is now traveling at a constant velocity, in a straight line.Snow is falling vertically (as seen by a person standing still on the ice), and the snow is accumulating on the sled. You have three strategies fortrying to keep the sled moving as fast as possible:

a)Sweep the snow off the sled so that it leaves the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of the sled.
b) Sweep the snow off the sled so that it leaves the sled in the direction perpendicular to the sled's
motion,as seen by you in the reference frame of someone standing still on the ice.
c) Do nothing.
Rank the strategies in effectiveness and explain your reasoning.

To rank the strategies in terms of their effectiveness in keeping the sled moving as fast as possible, we need to analyze the impact of each strategy on the sled's motion.

a) Sweeping the snow off the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of the sled:
By sweeping the snow off the sled in a direction perpendicular to its motion as seen from the sled, you are effectively removing the snow's momentum that was added to the sled. Since the sled is already moving at a constant velocity, any additional momentum from the fallen snow would slow it down. Therefore, strategy (a) would be the most effective in maintaining the sled's speed.

b) Sweeping the snow off the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of someone standing still on the ice:
In this scenario, you are considering the reference frame of someone standing still on the ice. When you sweep the snow off the sled in a direction perpendicular to its motion in this reference frame, you are essentially throwing the snow in the opposite direction of the sled's velocity. This action would transfer momentum from the sled to the snow, causing a minuscule slowdown in the sled's motion. However, since the sled is moving at a constant velocity, the effect on its speed would be negligible compared to strategy (a).

c) Doing nothing:
Choosing not to sweep the snow off the sled and leaving it to accumulate may have an impact on the sled's speed. As the snow accumulates, it increases the sled's mass. According to Newton's second law of motion, F = ma, if the applied force (the push) remains constant (as stated in the problem), an increase in mass would result in a decrease in acceleration. However, since the sled is already moving at a constant velocity, the accumulated snow's mass would not affect its speed directly. Therefore, doing nothing (strategy c) would have the least impact on the sled's speed.

In summary, ranking the strategies in terms of their effectiveness in maintaining the sled's speed while snow accumulates:
1) Strategy (a): Sweep the snow off the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of the sled.
2) Strategy (b): Sweep the snow off the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of someone standing still on the ice.
3) Strategy (c): Do nothing.

Ranking the strategies in effectiveness:

1) Strategy a) - Sweep the snow off the sled so that it leaves the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of the sled.

This strategy would be the most effective in maximizing the sled's speed. By sweeping the snow off perpendicularly to the sled's motion, there would be no change in the sled's momentum. The snow would simply transfer outwards, resulting in minimal disturbance to the sled's motion.

2) Strategy b) - Sweep the snow off the sled so that it leaves the sled in the direction perpendicular to the sled's motion, as seen by you in the reference frame of someone standing still on the ice.

While this strategy is similar to strategy a) in terms of sweeping the snow off perpendicularly to the sled's motion, as seen from the perspective of someone standing still on the ice, there might be a slight backward force applied on the sled due to the action of sweeping. This could result in a slight reduction in the sled's velocity compared to strategy a). However, the difference here may not be significant.

3) Strategy c) - Do nothing.

This strategy would be the least effective in maximizing the sled's speed. By doing nothing, the accumulating snow would inevitably create frictional resistance between the sled and the ice. This friction would gradually slow down the sled and reduce its velocity over time.

Overall, strategy a) would be the most effective as it minimizes any changes in the sled's momentum during the process of snow removal. Strategy b) could still be relatively effective, but there may be a slight decrease in the sled's velocity due to the backward force applied during the sweeping motion. Strategy c) would be the least effective as it allows friction between the accumulating snow and the sled to slow down its motion.