Ram moves in the east direction at a speed of $6 \, m/s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \, m/s$. The magnitude of their relative velocity is ........ $m/s$.

An airplane airspeed indicator reads $100 \, m/s$ and its compass shows that it is heading $37^{\circ}$ east of north. The meteorological information provided to the navigator is that the wind velocity is $20 \, m/s$ towards east. The speed of the airplane relative to the ground is closest to ............ $\, m/s$.

Two particles $P_1$ and $P_2$ are moving with velocities $v_1$ and $v_2$ respectively. Which of the following statements about their relative velocity $v_{12}$ is true?

Explain this common observation clearly: If you look out of the window of a fast-moving train,the nearby trees,houses,etc.,seem to move rapidly in a direction opposite to the train's motion,but the distant objects (hilltops,the Moon,the stars,etc.) seem to be stationary. (In fact,since you are aware that you are moving,these distant objects seem to move with you).

$A$ steamboat goes across a lake and comes back $(a)$ on a quiet day when the water is still and $(b)$ on a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both days was the same,in which case will it complete the journey in lesser time?

Rain is falling vertically with a speed of $30\; m/s$. $A$ woman rides a bicycle with a speed of $10\; m/s$ in the north to south direction. What is the direction in which she should hold her umbrella?