A motorboat is observed to travel10kmph relative to earth in the direction 37deg north of east.If the velocity of boat due to the wind only is 2kmph westward and that due to current only is 4kmph southward,what is the magnitude and direction of the velocity of the boat due to its own power.

Vanya Saxena Grade: Upto college level

        A motorboat is observed to travel10kmph relative to earth in the direction 37deg north of east.If the velocity of boat due to the wind only is 2kmph westward and that due to current only is 4kmph southward,what is the magnitude and direction  of the velocity of the boat due to its own power.

8 years ago

Answers : (2)

AskIITians Expert PRASAD IIT Kharagpur

18 Points

										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.

8 years ago

Ramesh V

70 Points

										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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