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AravindG
 4 years ago
10. The smoke emitted from a steamer, sailing due south, extends in a direction making an angle of 30⁰, north of west, while that from another steamer, sailing due north, with same speed, extends in a direction making an angle
Of 30⁰, west of south. If v be the speeds of each steamer, find the true velocity of wind.
AravindG
 4 years ago
10. The smoke emitted from a steamer, sailing due south, extends in a direction making an angle of 30⁰, north of west, while that from another steamer, sailing due north, with same speed, extends in a direction making an angle Of 30⁰, west of south. If v be the speeds of each steamer, find the true velocity of wind.

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0Here's what I got...dw:1327860852617:dwV1 and V2 are the velocities of the first and second ships respectively. S1 and S2 are the velocities of the smoke. The way I see it we have a system of equations based on these vectors if we notice that the smokes vectors are the sum of the ship and wind vectors.\[S_{1}=V_1+W\to W=S_1V_1\]\[S_2=V_2+W\to W=S_2V_2\]the magnitude on each speed vector the the boats is the same, so we have\[S_1V_1=<S_1\cos\theta_1,S_1\sin\theta_1><0,V>\]\[=<S_1\cos\theta_1,S_1\sin\theta_1+V>\]\[S_2V_2=<S_2\cos\theta_2,S_2\sin\theta_2><0,V>\]\[=<S_2\cos\theta_2,S_2\sin\theta_2V>\]these are equal quantities (both equal to wind) so by treating their components separately we can create the following system\[S_1\cos\theta_1S_2\cos\theta_2=0\]\[S_1\sin\theta_1S_2\sin\theta_2=2V\]This system can be solved for S1 and S2 in terms of V. Once you have that you can use either of the earlier equations for W to find it in terms of the speed of the boat,

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.0...here are what I mean by theta 1 and 2 just to clarify:dw:1327862701263:dw
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