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A 6 kg6\,\text{kg} crate starts from rest at the top of a 12 m12\,\text{m} high platform (use g=10 m/s2g=10\,\text{m/s}^2). It slides down a frictionless track to the bottom, then moves across a rough horizontal floor for 8 m8\,\text{m} where the kinetic friction force is constant at 30 N30\,\text{N}, and then goes up a frictionless ramp to a final point where it comes to rest. What maximum vertical height above the floor does the crate reach on the ramp? (Track energy: initial PEg→PE_g \to bottom KE→KE \to thermal loss on floor →\to final PEgPE_g.)
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