@ Anandghegde,
Before solving this problem just go through this link;
http://ocw.mit.edu/NR/rdonlyres/Aeronautics-and-Astronautics/16-07Fall-2004/EDABC2D9-6030-4F56-B369-D6CEE666F502/0/d27.pdf
And make sure that you are perfect with all the concepts in it.
Let us proceed,
As we know,
Given, Lambda (L) = dm/dt
As, Fth = (dm/dt) u
Thus, we have,
Fth = Lu .. (i)
The direction of Fth will be in the opposite direction of u, because the system is loosing mass.
We also have variable mass = M - Lt .. (ii)
Draw the FBD and resolve Fth along x and y coordinates as shown in the Figure.
Along y coordinate, we have,
N = Fth sin 0 + (variable mass) g
Substitute (i) and (ii), we have,
N = Lu sin 0 + (M - Lt) g ..(iii)
Frictional force f = µ N ..(iv)
Along x coordinate, we have,
Fth cos 0 - f = (dv/dt)(variable mass)g
Substitute (i), (ii), (iii) and (iv), we have
Lu cos 0 - µ [Lu sin 0 + (M - Lt) g] = (dv/dt)(M - Lt) g
Multiply throughout by dt and and divide by (M - Lt)
And then integrate LHS from zero --> t and RHS from zero --> v
The sign 0t{ indicates integration from zero --> t
0t{ Lu cos 0 dt / (M - Lt) - 0t{ µLu sin 0 dt / (M - Lt) + 0t{ µg dt = 0v{ dv
Therefore, we have
v = Lu cos 0 ln | M / (M - Lt) | - µLu sin 0 ln | M / (M - Lt) | - µgt
Take ln | M / (M - Lt) | common and you will get the final answer.
I believe that whatever I have solved is correct. Nudge me if you have any query.
Dude, you are in XIth with me; you should have tried it yourself. Nevermind !!!
