$A$ boy standing on the footpath tosses a ball straight up and catches it. The driver of a car passing by,moving with uniform velocity,sees this. The trajectory of the ball as seen by the driver will be:

Two particles $A$ and $B$ are moving in a horizontal plane as shown in the figure at $t = 0$. The time after which $A$ will catch $B$ is.......$s$.

Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100 \text{ km/h}$ and $80 \text{ km/h}$, respectively, such that car $A$ is moving ahead of car $B$. $A$ person in car $B$ throws a stone with a speed $v$ so that it hits car $A$ with a speed of $5 \text{ m/s}$. The value of $v$ is . . . . . . $\text{km/h}$.

$A$ river is flowing from west to east with a speed of $9 \ km \ h^{-1}$. $A$ boat, capable of moving at a maximum speed of $27 \ km \ h^{-1}$ in still water, crosses the river in half a minute. If the boat moves at an angle of $150^{\circ}$ to the direction of the river flow, then the width of the river is:

The width of the river is $1 \; km$. The velocity of the boat is $5 \; km/hr$. The boat covers the width of the river along the shortest possible path in $15 \; min$. The velocity of the river stream is:

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?