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 Originally Posted by MadMojoMonkey
Since one rate traverses more distance than the other in the same time, it requires more force in the same time, meaning greater impulse.
Other than that, my analysis holds.
I don't understand what you mean here. If you resolve gravity into the directions parallel and perpendicular to the slope then you will find out what force is needed (propulsion) for constant speed. This gravitational force should not be speed dependent. With no friction, the required propulsion force should also not be speed dependent.
The way I would look at this is that with speed constant, you are increasing gravitational potential energy (mass x g x height). Cyclist 2 will increase height faster than cyclist 1, so he will convert weetabix energy into potential energy faster. If he moves twice as fast then he uses energy twice as fast.
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