Question

The ratio VA/VB is equal to?

Answer 1

VA/vb=cos sign of theta

Answer 2

The ratio of velocities of ship A to ship B is cosθ.

Figure shows two ships moving in x-y plane with velocities VA and VB. The ships moves such that B always remains north of A.

We have to find the ratio of VA/VB.

Conceptual point : According to question, B always remains north of A. It means, the horizontal component of velocity of ship B must be the same of velocity of ship A.

   Here velocity of ship B is inclined at an angle θ with the horizontal line.

• So the component of velocity of ship along vertical line = VBsinθ
• And the component of velocity of ship B along horizontal line = VB cosθ

$\implies V_A=V_B\:\:[\text{along x-axis}]$

$\implies V_A=V_Bcos\theta\\\\\implies\frac{V_A}{V_B}=cos\theta$

Therefore the ratio of velocities of ship A to ship B is cosθ.

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