Relative Velocity MCQs for NEET

The velocity of moving objects with respect to other moving or stationary objects is called “relative velocity.”

The relative velocity of an observer B in the rest frame of another observer A is given by the formula:

Relative velocity of B relative to A = $\vec{v_b}-\vec{v_a}$

If both the objects are moving in the same direction, then

$\vec{v_{ab}}=\vec{v_a}+\vec{v_b}$

If the objects are moving in the opposite direction, then

$\vec{v_{ab}}=\vec{v_a}-\vec{v_b}$

1. Two bikes travelling in the same direction move at a speed of 30 km/hr. The bikes are separated by a distance of 5 km. What would the speed of the car travelling in the opposite direction be if it meets these bikes at an interval of 4 minutes?

1. 40 km/hr
2. 45 km/hr
3. 30 km/hr
4. 15 km/hr

2. On a rainy day, a girl standing on the road has to hold her umbrella at an angle of 300 with respect to the vertical to avoid getting drenched in the rain. She throws the umbrella and starts running at a speed of 10 km/hr. She notices that the raindrops are falling vertically on her head. What is the speed of the raindrops with respect to the ground?

1. 20 km/hr
2. 10 km/hr
3. 30 km/hr
4. 40 km/hr

3. In the above problem, the speed of raindrops w.r.t to the moving girl is

1. $\frac{10}{\sqrt{2}}\,km/hr$
2. $\frac{5}{\sqrt{3}}\,km/hr$
3. $10\sqrt{3}\,km/hr$
4. $5\,km/hr$

Answer: (c) $10\sqrt{3}\,km/hr$

4. A 150 m long train moves towards south at a speed of 10 m/s. A sparrow flying at a speed of 5 m/s towards north crosses the train. What is the time taken by the sparrow to cross the train?

1. 30 s
2. 15 s
3. 8 s
4. 10 s

5. A river flows east to west at a speed 5 m/min. A man capable of swimming 10 m/min in still water is standing on the south bank of the river. He wants to swim across the river in the shortest time possible. Which of the following path should he choose?

1. Due North
2. Due North-East
3. Due North-East with double the speed of the river
4. None of the above

6. A person who aims to reach the exact opposite point on the bank of a stream swims at a speed of 0.5 m/s at an angle of 1200 following the direction of the water flow. What is the speed of water in the stream?

1. 1 m/s
2. 0.25 m/s
3. 0.5 m/s
4. 0.433 m/s

7. X moves at a speed of 65 km/hr while Y who is behind X moves at a speed of 80 km/hr. What is the relative velocity of Y with respect to X?

1. 60 km/hr
2. 80 km/hr
3. 145 km/hr
4. 15 km/hr

8. A person who aims to reach the exact opposite point on the bank of a stream swims at a speed of 0.5 m/s at an angle of 1200 following the direction of the water flow. What is the speed of water in the stream?

1. 1 m/s
2. 0.5 m/s
3. 0.25 m/s
4. 0.433 m/s

9. A deer being preyed upon by the lion runs at a speed of 9 m/s. The lion chases the deer running at a speed of 10 m/s. If the instantaneous separation of deer from the lion is 100 m. How long would it take the lion to catch the deer?

1. 1 second
2. 19 seconds
3. 90 seconds
4. 100 seconds