What Is the Realistic Horsepower of a Truck Climbing Rabbit Ears Pass?

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The discussion centers on calculating the horsepower required for a 40,000 kg truck to climb Rabbit Ears Pass while maintaining a speed of 50 mph. The initial calculation yielded an unrealistic horsepower figure of 57,442, leading to concerns about potential errors in unit conversion or the height measurement. Participants suggest focusing on the vertical speed and using consistent units, such as meters, seconds, and kilograms, to ensure accuracy. The importance of correctly applying the formulas for power and work is emphasized, particularly regarding the change in elevation. Accurate calculations are crucial for determining the realistic horsepower needed for the climb.
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A 40,000 kg truck traveling on I-70 leaves Denver (elevation 5280', mile marker 244) and goes over Rabbit Ears pass (elevation 11,840', mile marker 238) while maintaining 50 mph. What is the horse power rating on his engine?


The formulas I used are as follows:

power = work/time

work = (mass)(gravity)(height)

746 watts = 1 horsepower

To solve for time I did 50 miles/60 minutes = 6 miles/x minutes and got 7.2 minutes (or 432 seconds).

After putting in all of these numbers I got 57,442 horsepower. This doesn't seem to make sense though, as that is a LOT of horsepower. I think the problem may be the height, since I put in the change of height (6560 feet). Help please? Suggestions?
 
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Put everything into metres, seconds and kg, I suspect you have got the units mixed up.

Hint - you only care about the vertical speed.
 

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