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Conservation of Energy and Ramps

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A truck of mass m has a brake failure while going down an icy mountain road with downward slope angle a. Initially the truck is moving downhill at speed V(0). After careening downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle B. The truck ramp has a soft sand surface for which the coefficient of rolling friction is u(r). What is the distance that the truck moves up the ramp before coming to a halt?

Please see attached file for full problem description along with the diagram.

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Solution Summary

Response uses energy methods to compute the answer.

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Please refer to the attached file.

Initially, the truck possesses potential energy and kinetic energy. So, we need to find its height into order to determine its potential energy.

Height = h = L sin a
So, ...

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