# Velocity of a trolley on an inclined plane with a twist

1. Mar 2, 2010

### sriram_15_93

A friend asked me how to solve this problem:

There is a trolley of mass M$$_{o}$$kg on a fixed inclined plane, whose angle of inclination is $$\theta$$. The block is at a height Hmetres, at the top of the inclined plane. Coefficient of friction is $$\mu$$. It is also known that it is raining, and the rain drops are falling with a velocity ums$$^{-1}$$ at the rate of $$\eta$$ kgs$$^{-1}$$. The rain is also falling, making an angle $$\alpha$$ with the ground. The trolley is released from rest at t=0. Find the velocity v of the trolley when it reaches the bottom.

I solved this question and ended up with a big differential equation in terms of dv and dt. However, part of the equation contains a dx (displacement along the plane) with t in the denominator that I am unable to get rid of. The only way I can do so is by means of a relation between displacement and time. Could someone help me with this part?

The problems I'm facing are:
(i) acceleration is varying
(ii) velocity is varying
(iii) I'm unable to get a constraint independent of velocity of the trolley.

I've attached a .bmp of the figure. Hope it helps.

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