Rope Sliding on Double Ramp

A $$\SI{1}{\kilo\gram}$$ rope of length $$\SI{1.5}{\meter}$$ slides down a frictionless double ramp in the shape of an equilateral triangle, as shown in the diagram above. At time $$t = 0$$, the rope is at rest with $$\SI{1}{\meter}$$ of its length on the right side of the ramp.

How much time (in seconds, to 3 decimal places) elapses before all of the rope is on the right side?


Details and Assumptions:

• The downward gravitational acceleration is $$\SI[per-mode=symbol]{10}{\meter\per\second\squared}.$$
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