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## Homework Statement

a car's engine, producing a constant power, propels the car up a hill at a constant speed and down the hill at double the speed. if the coefficient of kinetic friction between the car and the road is 0.28, what is the angle of incline of the hill. assume the hill is symmetric.

## Homework Equations

## The Attempt at a Solution

While going upwards, friction and weight component are acting downwards.

∴Ef=Ff+mgsinθ

Ef=μN+mgsinθ

=μmgcosθ +mgsinθ

While going downwards, the frictional force reverses direction. but the velocity is double....So i am assuming that the downwards force is double.

∴2Ff=mgsinθ+Ef

Ef=2μmgcosθ-mgsinθ

equate the two expressions:

μmgcosθ +mgsinθ=2μmgcosθ-mgsinθ

2mgsinθ=2μmgcosθ

tan θ=μ=0.28

θ=tan(-1) 0.28

=15.64 degrees