Coefficient of friction of a ramp

[maladroit]

Homework Statement

A student has two ramps, both of which are at an angle of 30o. Ramp 1 is frictionless and ramp 2 has friction. The student also has two blocks, one for each ramp. She pushes the blocks up the ramps with the same initial velocity. The block on ramp 2 only travels a fraction f = 0.625 as far as the block on ramp 1 before coming to a stop (i.e. d2 = 0.625*d1) .

Homework Equations

Ff=\muFn
v2^2-v1^2=2ad

The Attempt at a Solution

I am way stuck on this!

 

[rl.bhat]

Hi maladroit, welcome to PF.
While posting any problem, state it completely as it is given in the home work.
In the above problem what is required? Are the two blocks identical?

 

[maladroit]

That is exactly as the problem is written, the only thing I forgot to include was that we are looking for the coefficient of friction. Sorry about that!

 

[rl.bhat]

In the ramp 1, the retardation is g*sinθ.
Initial velocity is v and the final velocity is zero. So
v^2 = 2*g*sinθ*d
In the second case, the normal reaction is mgcosθ and frictional force = μmgcosθ.
So the net retardation is (g*sinθ + μgcosθ)
Now write down the expression for v^2 and solve for μ.

 

[maladroit]

Thank you so much for the help!