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

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:

$$V _ {b} = 5 \frac {m}{s} - \text{speed of the bird};$$ $$V _ {w} = 3 \frac {\dot {m}}{s} - \text{speed of the wind};$$

Relative velocity of the bird with respect to the wind is the difference between vectors of the bird's and the wind's velocities:

$$\overline {v} _ {b, w} = \overline {v} _ {b} - \overline {v} _ {w} = \overline {v} _ {b} + (- \overline {v} _ {w})$$

Hypotenuse of the right triangle ABC:

$$\begin{array}{l} \left| \overline {v} _ {b, w} \right| = \sqrt {\overline {v} _ {b} ^ {2} + \overline {v} _ {w} ^ {2}} = \sqrt {\left(5 \frac {m}{s}\right) ^ {2} + \left(3 \frac {m}{s}\right) ^ {2}} = \sqrt {3 4} \frac {m}{s} \\ = 5. 8 \frac {m}{s} \\ \end{array}$$

Answer: relative velocity of the bird with respect to the wind is $5.8\frac{m}{s}$.