$A$ bus appears to go with a speed of $25 \, km/hr$ to a car driver,driving at the rate of $7 \, km/hr$ northwards. If the bus actually travels in the east direction,its speed is ......... $km/h$.

The velocities of $A$ and $B$ are $\vec{v}_A = 2 \hat{i} + 4 \hat{j}$ and $\vec{v}_B = 3 \hat{i} - 7 \hat{j}$. The velocity of $B$ as observed by $A$ is:

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

$A$ man standing on a road has to hold his umbrella at $30^{\circ}$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \,km/h$. He finds that raindrops are hitting his head vertically. The actual speed of raindrops is:

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.......$s$.

$A$ 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: