Block going up a frictionless incline

[Momentum09]

Homework Statement

A 2.6kg block slides along a frictionless horizontal with a speed of 2.9m/s. After sliding a distance of 6m, the block makes a smooth transition to a frictionless ramp inclined at an angle of 12 degrees to the horizontal. How far up the ramp does the block slide before coming momentarily to rest?

Homework Equations

Conservation of mechanical energy...1/2mv0^2 + mgh0 = 1/2mvf+mghf.

The Attempt at a Solution

I know that V0 = 26, Vf = 0, but I don't know what h is. Is there another approach to this problem?

Thank you so much!

 

[Doc Al]

Realize that you can express the final position in terms of height or distance up the ramp: those two distances are connected by a little trig.

In any case, you can solve for the final height, then convert to the needed distance up the ramp.