$A$ $120 \, m$ long train is moving towards west with a speed of $10 \, m/s$. $A$ bird flying towards east with a speed of $5 \, m/s$ crosses the train. The time taken by the bird to cross the train will be ........ $sec$.

The speed of a swimmer in still water is $20 \; m/s$. The speed of river water is $10 \; m/s$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path,the angle at which he should make his strokes with respect to north is given by ......$^o$ west.

If the velocities of particles $A$ and $B$ with respect to the ground are ${\overrightarrow v _A}$ and ${\overrightarrow v _B}$ respectively,then:
$(a)$ Write the formula for the velocity of $A$ with respect to $B$.
$(b)$ Write the formula for the velocity of $B$ with respect to $A$.
$(c)$ Is the relation ${\overrightarrow v _{AB}} = -{\overrightarrow v _{BA}}$ correct?

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days,if she remains stationary on the moving escalator,then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

$A$ river of width $200 \ m$ is flowing from west to east with a speed of $18 \ km/h$. $A$ boat,moving with a speed of $36 \ km/h$ in still water,is made to travel one round trip (bank to bank of the river). The minimum time taken by the boat for this journey and the displacement along the river bank are . . . . . . and . . . . . . respectively.

Two cities $X$ and $Y$ are connected by a regular bus service with a bus leaving in either direction every $T$ min. $A$ girl is driving a scooty with a speed of $60 \ km/h$ in the direction $X$ to $Y$ and notices that a bus goes past her every $30$ minutes in the direction of her motion,and every $10$ minutes in the opposite direction. Choose the correct option for the period $T$ of the bus service and the speed (assumed constant) of the buses.