Question

A bird flies in the east direction with a speed of 5 ms−1. The wind is blowing towards north at a
speed of 3 ms−1. Determine the relative velocity of the bird with respect to the wind. Draw
appropriate diagram for solving the problem.

Answer 1

Question:

A bird flies in the east direction with a speed of 5 ms-1. The wind is blowing towards north at a speed of 3 ms-1. Determine the relative velocity of the bird with respect to the wind. Draw appropriate diagram for solving the problem.

Solution:

We will use a Galilean addition of velocities:

$$\overrightarrow {V} = \overrightarrow {V _ {0}} + \overrightarrow {V ^ {\prime}},$$

where $\vec{V} = \vec{V}_b$ - the velocity of the bird with respect to the stationary coordinate system;

$\vec{V} = \vec{V}_w$ - the velocity of the moving coordinate system with respect to the stationary coordinate system;

$\vec{V}^{\prime}$ - the velocity of the bird with respect to the wind (moving coordinate system);

From the law of cosines:

$$V ^ {\prime 2} = V _ {w} ^ {2} + V _ {b} ^ {2} - 2 \cdot V _ {w} \cdot V _ {b} \cdot \cos \alpha = 3 ^ {2} + 5 ^ {2} - 2 \cdot 3 \cdot 5 \cdot \cos 9 0 ^ {0} = 9 + 2 5 - 2 \cdot 3 \cdot 5 \cdot 0 = 3 4$$

Answer: $V' \approx 5.8 \frac{m}{s}$