### Relative Velocity Problems Worksheet:

**Ques. **A jet airplane travelling at the speed of 500 km h^{-1} ejects its products of combustion at the speed of 1500 km h^{-1} relative to the jet plane. What is the speed of the later with respect to observer on the ground.

(a) – 1000 km/hr

(b) – 900 km/hr

(c) – 800 km/hr

(d) – 700 km/hr

**Ques. **Two bodies are moving in opposite directions with velocity *v*. The relative velocity of one w.r.t. the other is:

(a) zero

(b) *v
*(c) √2

*v*

(d) 2

*v*

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

(a) 105 m/s

(b) 55 m/s

(c) 20 m/s

(d) 75 m/s

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**Ques. **A train is moving eastwards with a velocity of 10 ms^{-1}. On a parallel track another train passes with a velocity 15 ms^{-1} eastwards. To the passengers in the second train, the first train will appear to be moving with a velocity:

(a) 5 ms^{-1} westwards

(b) 5 ms^{-1} eastwards

(c) 20 ms^{-1} westwards

(d) 25 ms^{-1} eastwards

**Ques. **Two trains A and B of length 400 m each are moving on two parallel tracks with a uniform speed of 72 km h^{-1} in the same direction with A ahead of B. The driver of B decides to overtake A and accelerate by 1 ms^{-2}. If after 50 s, the guard of B just brushes past the driver of A, what was the original distance between them?

(a) 480 m

(b) 450 m

(c) 420 m

(d) 400 m

**Ques. **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, with what speed does the bullet hits the thief’s car?

(a) 105 m/s

(b) 55 m/s

(c) 20 m/s

(d) 75 m/s

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**Ques. **A man can swim with a speed of 4 km/h in still water. How long does he take to cross a river 1 km wide if the river flows steadily at 3 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?

(a) 780 m

(b) 750 m

(c) 720 m

(d) 700 m

**Ques. **A bucket is placed in the open where the rain is falling vertically. If a wind begins to blow at double the velocity of the rain, how will be rate of filling of the bucket change?

(a) Remain unchanged

(b) Doubled

(c) Halved

(d) Become four times

**Ques. **On a two lane road, car A is travelling with a speed of 36 km h^{-1}. Two cars B and C approach car A in opposite directions with a speed of 54 km h^{-1} each. At a certain instant, when the distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident.

(a) 3 m/s^{2}

(b) 2 m/s^{2}

(c) 1 m/s^{2}

(d) 0.5 m/s^{2}

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**Ques. **A car is going eastwards with a velocity of 8 ms^{-1}. To the passengers in the car, a train appears to be moving north-wards with a velocity 15 ms^{-1}. What is the actual velocity of the train?

(a) 7 ms^{-1}

(b) 17 ms^{-1
}(c) 23 ms^{-1}

(d) None of these

**Ques. **A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of 12 km/h he observes that the rains is falling at an angle 60^{o} with the vertical. The actual velocity of rain is:

(a) 12√3 km/h

(b) 12 km/h

(c) 4√3 km/h

(d) 10√3 km/h

**Ques. **To a person going towards east in a car with a velocity of 25 km/h, a train appears to move towards north with a velocity of 25√3 km/h. The actual velocity of the train will be:

(a) 25 km/h

(b) 50 km/h

(c) 5 km/h

(d) 53 km/h

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**Ques. **Two particles P and Q simultaneously start moving from point A with velocities 15 m/s and 20 m/s respectively. The two particles move with accelerations equal in magnitude but opposite in direction. When P overtakes Q at B then its velocity is 30 m/s. The velocity of *Q* at point B will be:

(a) 30 m/s

(b) 5 m/s

(c) 20 m/s

(d) 15 m/s

**Ques. **Two particles start from rest simultaneously and are equally accelerated. Throughout t he motion, the relative velocity of one w.r.t. other is:

(a) zero

(b) non-zero and directed parallel to acceleration

(c) non-zero and directed opposite to acceleration

(d) directed perpendicular to the acceleration

**Ques. **Two rods cross at right angle at *O*. A person walking along one of them at 3 km/hr sees another person B walking at 4 km per hour along the other road at *O* when he is 100 m off. They are nearest to each other certain moment when A has walked a distance of :

(a) 63 m

(b) 36 m

(c) 22 m

(d) 11 m

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**Ques. **A beautiful girl is going eastwards with a velocity of 4 km/h. The wind appears to blow directly from the north. She doubles her speed and the wind seems to come from north east. The actual velocity of wind is:

(a) 4√2 km/h towards south east

(b) 4√2 km/h towards north west

(c) 2√2 km/h towards south east

(d) none of the above

**Ques. **A train of 150 m length is going towards north at a speed of 10 m/s. A bird flies at a speed of 5 m/s towards south parallel to the railway track. The time taken by the bird to cross the train will be equal to:

(a) 10 sec

(b) 12 sec

(c) 16 sec

(d) 20 sec

**Ques. **Two particles are moving with velocities *v*_{1} and *v*_{2}. Their relative velocity is the maximum when the angle between their velocities is:

(a) zero

(b) *π* / 4

(c) *π* / 2

(d) *π*

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**Ques. **Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the deceleration to be uniform and equal. The value of deceleration to barely avoid collision should be:

(a) 0.8 m/s^{2}

(b) 2.1 m/s^{2
}(c) 11.8 m/s^{2}

(d) 11.0 m/s^{2
}

**Ques. **From an elevated point *A*, a stone is projected vertically upwards. When the stone reaches a distance *h* below *A*, its velocity is double of what it was at a height above *A*. The greatest height attained by the stone is:

(a) h/3

(b) 2h/2

(c) h/2

(d) 5h/3

**Ques. **To a man walking at the rate of 3 km/h the rain appears to fall vertically. When he increases his speed to 6 km/h it appears to meet him at an angle of 45^{o} with vertical. Find the speed of rain.

(a) 3 km/h

(b) √2 km/h

(c) 3√2 km/h

(d) 3/√2 km/h

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**Ques. **The wind appears to blow from the north to a man moving in the north-east direction. When he doubles his velocity the wind appears to move in the direction cot^{-1} (2) east of north. The actual direction of the wind is:

(a) √2*v* towards east

(b) *v*/√2 towards west

(c) √2*v* towards west

(d) *v*/√2 towards east