A piece of ice slides down a 45degree incline in twice the time it takes to slide down a frictionless 45 degree incline. Find the coefficient of friction between the ice and the incline

The force towards the incline is mgsinθ. Now if there is friction then frictional force is μmgcosθ. So total downwards force on ice block coming with friction is mgsinθ-μmgcosθ. So the acceleration without friction and with friction are gsinθ and gsinθ-μgcosθ. Now suppose the length of the incline is S, then time taken by a body to travel distance S with acceleration a is t=2Sa. So the two times are
t1=2sgsinθ
and
2Sgsinθ-μgcosθ
Now dividing this two equation we get
gsinθgsinθ-μgcosθ=2
or 11-μtanθ=2
putting θ=45° we get
4-4μ=1
or μ=34

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