East -  i vector  North - j vector.

Vel of boat = vel of itself  + vel of wind + vel of current.

V_b = V_it + V_w + V_r

10(cos 37 i  + sin 37 j) = V_it  + (-2 i) + (-4 j)

8 i + 6 j = V_it  + (-2 i) + (-4 j)

V_it = 10 i + 10 j

Boat travels at 14.14 kmph 45deg north of east due to its owm power.

vel. of boat w.r.t wind V_bw = -2j

vel. of boat w.r.t water current V_bc = -4i

given vel. of boat w.r.t earth(water current + wind): V_b(w+c) = 6i + 8j

so, V_b - V_w = -2j                   .............(1)

       V_b - Vc = -4i                   .............(2)

       V_b - V(_w+c) = 6i + 8j     . ............(3)

Let vel. of boat alone due to its power is = (ai+bj)

From above (1) + (2) -(3) gives

V_b = -10.(i + j)

The magintude of vel. of boat = 14.14 kmph

direction is 45 degrees south west

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Naga Ramesh
IIT Kgp - 2005 batch