A friend asked me how to solve this problem:(adsbygoogle = window.adsbygoogle || []).push({});

There is a trolley of massM[tex]_{o}[/tex]kgon a fixed inclined plane, whose angle of inclination is [tex]\theta[/tex]. The block is at a heightHmetres, at the top of the inclined plane. Coefficient of friction is [tex]\mu[/tex]. It is also known that it is raining, and the rain drops are falling with a velocityums[tex]^{-1}[/tex] at the rate of [tex]\eta[/tex]kgs[tex]^{-1}[/tex]. The rain is also falling, making an angle [tex]\alpha[/tex] with the ground. The trolley is released from rest att=0. Find the velocityvof the trolley when it reaches the bottom.

I solved this question and ended up with a big differential equation in terms ofdvanddt. However, part of the equation contains adx(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 ofa 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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# Homework Help: Velocity of a trolley on an inclined plane with a twist

Can you offer guidance or do you also need help?

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