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is 55 MPH greater going uphill, downhill, or flat

February 4, 2011

Joe asks:

Is a vehicle going 55 mph downhill going faster than a vehicle going 55 on flat land? I just wonder because people seem to slow down going downhill in the mountains as compared to traveling on relatively flat land. Which then begs the question… heaven forbid… if a person were involved in an accident traveling 55 downhill would the forces exerted at impact be greater than traveling at 55 on flat land. I’m reminded of a mashed potato analogy in astronomy class 30 some odd years ago dealing with mass.

It wouldn’t make any difference. 55mph is the same downhill, uphill, or flat – speed is  not dependent on the slope of the ground. In a collision, the forces involved are going to be a result of the difference in the vectors of the two objects. In order to figure out the details, you’d need to do a vector analysis in 3D. Most High school physics courses should cover 2D collisions (or at least simple models of them). In the real world, things are a bit more complex – you need to take into account the deformation of the objects that are colliding, and a bunch of other variables (including the fact that the real world is 3D not 2D). In any case, the bottom line is that 2 objects colliding at a given speed and impact angle will have the same energy transfer. Going uphill or downhill will make some difference, but not much (this is the 3D part, and gravity plays into it). This is because the force of the vertical gravity vector would be added to the object going downhill, and subtracted from the object going uphill. For the slopes normally found on roads (including mountain roads) this wouldn’t be much.

Doctor Science

 

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