Relative Velocity

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 the car $A$ with a speed of $5\text{ m/s}$. The value of $v$ is $\underline{\qquad}\text{ km/h}$.

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 scooty with a speed of $60\text{ km/h}$ in the direction $X$ to $Y$ 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.

Train A is moving along two parallel rail tracks towards north with speed $72\text{ km/h}$ and train B is moving towards south with speed $108\text{ km/h}$. Velocity of train B with respect to A and velocity of ground with respect to B are (in $\text{ms}^{-1}$):

Two trains, each $30\text{ m}$ long are travelling in opposite directions with velocities $5\text{ m/s}$ and $10\text{ m/s}$. They will cross after

A passenger sitting in a train A moving at $90\text{ km/h}$ observes another train $B$ moving in the opposite direction for $8\text{ s}$. If the velocity of the train B is $54\text{ km/h}$, then length of train B is:

Two trains 'A' and 'B' of length '$l$' and '$4l$' are travelling into a tunnel of length '$L$' in parallel tracks from opposite directions with velocities $108\text{ km/h}$ and $72\text{ km/h}$, respectively. If train 'A' takes $35\text{ s}$ less time than train 'B' to cross the tunnel, then length '$L$' of tunnel is:

(Given $L = 60l$)

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be:

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms–1) of this person as observed from train B will be close to:

(take the distance between the tracks as negligible)

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite direction is:

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On another day, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

A Person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator?

A bus is moving with a speed of 10 ms${}^{-1}$ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

A train of 150 metre length is going towards north direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards south direction parallel to the railways track. The time taken by the parrot to cross the train is