$A$ $150\, m$ long train is moving to the north at a speed of $10\, m/s$. $A$ parrot flying towards the south with a speed of $5\, m/s$ crosses the train. The time taken by the parrot to cross the train would be........$s$.

$A$ stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of $12 \ km/h$,he observes that the rain is falling at an angle of $60^{\circ}$ with the vertical. The actual velocity of the rain is:

$A$ butterfly is flying with a velocity $4 \sqrt{2} \, m/s$ in the North-East direction. The wind is blowing at $1 \, m/s$ from North to South. The resultant displacement of the butterfly in $3 \, s$ is $.... \, m$.

$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \text{ m}$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \text{ m}$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \text{ m/s}$ and $v_2 = (a \hat{i} + 7 \hat{j}) \text{ m/s}$. If they collide after $2 \text{ s}$,then the value of $a$ is:

$A$ person walks up a stalled escalator in $90 \, s$. When just standing on the same moving escalator,he is carried in $60 \, s$. The time it would take him to walk up the moving escalator will be $....... \, s$.