Question

Wind blowing from south at 10m/s but to a cyclist it appears to be blowing from the east at 10m/s . The cyclist has a velocity

Answer 1

The velocity of the cyclist is $\bold{10 \sqrt{2} \mathrm{m} / \mathrm{s}}$  

To find:

The velocity of cyclist.

Solution:

By using the Velocity addition formula,

          If a wind is blowing relative to the cyclist with velocity 10 m/s from east $\overrightarrow{\mathrm{v}}$ and wind is blowing relative to ground with velocity 10 m/s from south $\overrightarrow{\mathrm{u}}$ , then the velocity of the cyclist is relative to ground which equals to the vector sum.

$\overrightarrow{\mathrm{s}}=\overrightarrow{\mathrm{v}}-\overrightarrow{\mathrm{u}}$

Pythagorean Theorem:

$s^{2}=u^{2}+v^{2}$

$=10 \sqrt{2} \mathrm{m} / \mathrm{s}$      

And the cyclist is directed to the direction of north-east.

Answer 2

Answer:

10√2 meter per second North east direction