Question

Wind is blowing from the south at 10 m/s but to a cyclist it appears to be blowing from the east at 10 m/s. The cyclist has a velocity?
(A) $10\widehat{i}-10\widehat{j}$\[\]
(B) $10\widehat{i}+10\widehat{j}$
(C) $-10\widehat{i}+10\widehat{j}$
(D) $-10\widehat{i}-10\widehat{j}$

Answer 1

Hint: Here in actual the wind is blowing from south but to the cyclist it appears to be blowing from the east. This means we have to use the concept of relative velocity. Relative velocity is defined as the measurement of velocity of a body with respect to some other body which is also in motion and not in rest. The frame of reference can move either at constant velocity or in an accelerated motion.

Complete step by step answer:
Let us try to solve this using the concept of relative velocity.
Velocity of wind, ${{v}_{w}}=10\widehat{j}$
Relative velocity of wind with respect to the cyclist, ${{v}_{wc}}=-10\widehat{i}$
Let the velocity of the cyclist be $\overrightarrow{v}$, then the relative velocity of wind with respect to the cyclist is given by, $\overrightarrow{{{v}_{wc}}}={{\overrightarrow{v}}_{w}}-{{\overrightarrow{v}}_{c}}$
$\Rightarrow 10\widehat{j}=-10\widehat{i}-{{\overrightarrow{v}}_{c}}$
$\therefore {{\overrightarrow{v}}_{c}}=-10\widehat{j}-10\widehat{i}$

So, the correct option is D.

Note:We have taken direction from west to east as positive and from east to west as negative x axis. Similarly, direction from south to north as positive y axis and from north to south as negative y axis. Velocity is a vector quantity and in this, we have to consider the direction of motion. When a body moves with constant velocity then its acceleration is zero. Always while finding out the relative velocities, we have to be very careful with the direction and take the sign positive or negative.