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Ship \(A\) is travelling with a velocity of \(5~\text{km/h}\) due east. A second ship is heading \(30^\circ\) east of north. What should be the speed of the second ship if it is to remain always due north with respect to the first ship?
1. \(10~\text{km/h}\)
2. \(9~\text{km/h}\)
3. \(8~\text{km/h}\)
4. \(7~\text{km/h}\)

Subtopic:  Relative Motion |
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Level 1: 80%+
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Raindrops are falling vertically downward at a constant speed of \(4~\text{m/s}.\) A man running forward at \(4~\text{m/s}\) observes the raindrops falling with a velocity of:
 
1. \(8~\text{m/s}\) 2. zero
3. \(\begin{aligned}4\sqrt2~\text{m/s} \\ \end{aligned}\) 4. \(\cfrac{4}{\sqrt2}~\text{m/s}\)
Subtopic:  Relative Motion |
 84%
Level 1: 80%+
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A boat is moving with a velocity \(3\hat i+ 4\hat j\) with respect to ground. The water in the river is moving with a velocity \(-3\hat i- 4\hat j\) with respect to the ground. The relative velocity of the boat with respect to water is:
1. \(8\hat j\)
2. \(-6\hat i-8\hat j\)
3. \(6\hat i + 8\hat j\)
4. \(5\sqrt{2}\)

Subtopic:  Relative Motion |
 83%
Level 1: 80%+
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The speed of water in a river is \(4~\text{km/h}\) and a man can swim at \(5~\text{km/h}.\) The minimum time taken by the man to cross the river of width \(200~\text m\) is:

1. \(\dfrac{1}{5}~\text h\)

2. \(\dfrac{1}{25}~\text h\)

3. \(\dfrac{1}{15}~\text h\)

4. \(\dfrac{1}{20}~\text h\)

Subtopic:  Relative Motion |
 85%
Level 1: 80%+
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The speed of a boat is \(5\) km/hr in still water. It crosses a river of width \(1\) km along the shortest possible path in \(15\) minutes. The velocity of the river water is:
1. \(3\) km/hr
2. \(4\) km/hr
3. \(5\) km/hr
4. \(2\) km/hr

Subtopic:  Relative Motion |
 82%
Level 1: 80%+
AIPMT - 1998
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While falling freely through the air, two skydivers play catch with a ball. Ignoring air resistance, in which direction should one skydiver throw the ball, relative to the other, to ensure it is caught?
1. Above the other, since the ball will fall faster.
2. Above the other, since the ball will fall more slowly.
3. Below the other, since the ball will fall more slowly.
4. Directly at the other, since there is no air resistance.
Subtopic:  Relative Motion |
 82%
Level 1: 80%+
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A swimmer swims perpendicular to river flow and reaches point \(B\). If the velocity of the swimmer in still water is \(4\) km/hr, the velocity of the river flow is:
1. \(3\) km/hr 2. \(5\) km/hr
3. \(2\) km/hr 4. \(6\) km/hr
Subtopic:  Relative Motion |
 79%
Level 2: 60%+
JEE
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On a rainy day, a boy standing on the road finds that he needs to hold his umbrella at an angle of \(30^\circ\) with respect to the vertical to avoid getting drenched in the rain. He throws the umbrella and starts running at a speed of \(10\) km/h. He observes that the raindrops are falling vertically on his head. What is the speed of the raindrops with respect to the ground?
1. \(15\) km/h
2. \(20\) km/h
3. \(30\) km/h
4. \(35\) km/h

Subtopic:  Relative Motion |
 79%
Level 2: 60%+
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Two balls are thrown simultaneously at the same speed of \(20~\sqrt2~\text{m/s:}\) the first one \((A)\) at an angle of \(45^\circ\) below the horizontal and the second one \((B)\) at an angle of \(45^\circ\) above the horizontal. The first one \((A)\) is projected from the top of a building (height\(=20~\text{m}\)) while the second \((B)\) from the bottom – both in the same vertical plane, as shown. Take \(g=10~\text{m/s}^2,\) if required.
                                                 
The relative velocity and relative acceleration of the balls, are:
1. \(40~\text{m/s},20~\text{m/s}^2\) 2. \(40~\text{m/s},0~\text{m/s}^2\)
3. \(20~\text{m/s},20~\text{m/s}^2\) 4. \(20\sqrt2~\text{m/s},0~\text{m/s}^2\)
Subtopic:  Relative Motion |
 77%
Level 2: 60%+
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Two particles, \(A\) and \(B\) are projected into the air from the same point. Particle \(A\) is thrown with a speed of \(30~\text{m/s}\) and particle \(B\) with a speed of \(40~\text{m/s},\) as shown in the diagram. The separation between them after one second is:
1. \(50~\text{m}\) 2. \(100~\text{m}\)
3. \(30~\text{m}\) 4. \(40~\text{m}\)
Subtopic:  Relative Motion |
 76%
Level 2: 60%+
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