Relative Velocity

Q. A swimming duck paddles the water with its feet once every 1.6s, producing surface waves with this time period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32m/s, and the crests of the waves ahead of the duck are spaced 0.12m apart, (a) what is the duck’s speed? (b) How far apart are the crests behind the duck?

1. 0.245 m/s, 0.904 m
2. 0.350 m/s, 0.715 m
3. 0.44 m/s, 1.3 m
4. 0.12 m/s, 0.452 m

Q.

A police van moving on a highway with a speed of $30km{h}^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of $192km{h}^{-1}$. If the muzzle speed of the bullet is $150m{s}^{-1}$, with what speed does the bullet hit the thief's car? (Note: Obtainthat speed which is relevant for damaging the thief's car).

Q.

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed $9km{h}^{-1}$ (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of $4km{h}^{-1}$. For an observer on a stationary platform outside, what is the
a) speed of the child running in the direction of motion of the belt?
b) speed of the child running opposite to the direction of motion of the belt?
c) time taken by the child in (a) and (b) ?
Which of the answers alter if motion is viewed by one of the parents?

Q.

A police van moving on a highway with a speed of 30 km/ h fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km/ h. If the muzzle speed of the bullet is 150 m s–1, at what speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Q.

A steamer moves with a velocity 3 kmph in and against the direction of river water whose velocity is 2 kmph. Total time for total journey if the boat travels 2 km in direction of stream and then back to its place will be (in hour)

1. 2.4

2. 3

3. 2.5

4. 2

Q. The distance between two particles is decreasing at the rate of $6\frac{m}{sec}$. If these particles travel with same speeds as in previous case and in the same direction, then the separation increase at the rate of $4\frac{m}{sec}$. The particles have speeds as

1. 
2. 
3. 
4. 

Q.

A train is moving with a velocity of 100 km/hr. Car A is traveling with velocity 100km/hr w.r.t. train in the opposite direction. Car B is traveling at the rate of 100 km/hr on the ground alongside the train. A man X is sitting inside the train and a man Y is standing outside the train and watching the entire episode. With respect to who is the car A at rest?

1. Man X

2. Train

3. Car B

4. Man Y

Q.

Consider two cities P and Q between which consisted bus service is available in both the directions every 'x' minutes. A morning jogger is jogging towards Q from P with a speed of 10 km/hr. Every 18 minutes a bus crosses this jogger in its own direction of motion and every 6 minutes another bus crosses in opposite direction. What is the time between two consecutive buses and also find the speed of the buses?

1. 9 min, 15 km/hr

2. 9 min, 20 km/hr

3. 6 min, 20 km/hr

4. 6 min, 15 km/hr

Q.

Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up-stream. When the faster one overtakes the slower one, a buoy (floating device) is dropped from the slower one. After sometime both the boats turn back simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again. If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity is 1.5 m/s, find the distance( in metres) travelled by the buoy from the dropping point till the point where the boats meet the buoy again. ___

Q. A 210 meter long train is moving due North at a velocity of 25m/s. A small bird is flying due South a little above the train with speed 5m/s. The time taken by the bird to cross the train is

1. 6s
2. 7s
3. 9s
4. 10s