A man is walking on a horizontal road with a speed of $$4$$ km/h. Suddenly, the rain starts vertically downwards with a speed of $$7$$ km/h. The magnitude of the relative velocity of the rain with respect to the man is:
1. $$\sqrt{33}$$
km/h
2. $$\sqrt{65}$$ km/h
3. $$8$$ km/h
4. $$4$$ km/h

Subtopic: Â Relative Motion |
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A man is walking on the road with a speed $$3$$ m/s. Rain is falling vertically at speed $$3$$ m/s. At what angle from the vertical, man has to hold his umbrella to avoid the rain drops?
1. $$45^\circ$$
2. $$30^\circ$$
3. $$60^\circ$$
4. $$90^\circ$$
Subtopic: Â Relative Motion |
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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 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: Â Relative Motion |
Â 83%
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PMT - 1998
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Raindrops are falling with speed $$v$$ vertically downwards and a man is running on a horizontal road with speed $$u.$$ The magnitude of the velocity of the raindrops with respect to the man is:
1. $$v-u$$
2. $$v+u$$
3. $$\sqrt{{v}^2 + {u}^2 \over 2}$$
4. $$\sqrt{{v}^2 + {u}^2}$$

Subtopic: Â Relative Motion |
Â 82%
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A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of $$5$$ m/s at an angle of $$120^\circ$$ with the flow. The speed of the flow must be:
1. $$2.5$$ m/s
2. $$3$$ m/s
3. $$4$$ m/s
4. $$1.5$$ m/s

Subtopic: Â Relative Motion |
Â 83%
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A swimmer swims a distance d upstream in $$4$$ s and swims an equal distance downstream in $$2$$ s. The ratio of swimmer's speed in still water to the speed of river water will be:

 1 $$\frac{6}{5}$$ 2 $$\frac{3}{1}$$ 3 $$\frac{5}{3}$$ 4 $$\frac{4}{3}$$
Subtopic: Â Relative Motion |
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A man standing on a road holds his umbrella at $$30^{\circ}$$ with the vertical to keep the rain away. He throws the umbrella and starts running at $$10$$ km/hr. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be:
1. $$10$$ km/hr
2. $$20$$ km/hr
3. $$30$$ km/hr
4. $$40$$ km/hr

Subtopic: Â Relative Motion |
Â 76%
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A man can row a boat with a speed of $$10$$ kmph in still water. The river flows at $$6$$ kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width $$1$$ km is:
1. $$\frac{1}{8}~\text{h}$$
2. $$\frac{1}{4}~\text{h}$$
3. $$\frac{1}{2}~\text{h}$$
4. $$1~\text{h}$$

Subtopic: Â Relative Motion |
Â 72%
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When a man walks on a horizontal road with velocity $$1$$ km/h, the rain appears to him coming vertically at a speed of $$2$$ km/h. The actual speed of the rain with respect to ground is:
1. $$\sqrt{3}$$ km/h
2. $$\sqrt{5}$$ km/h
3. $$1$$ km/h
4. $$3$$ km/h

Subtopic: Â Relative Motion |
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A man is crossing a river flowing with a velocity of $$5$$ m/s. He reaches a point directly across the river at a distance of $$60$$ m in $$5$$ s. His velocity in still water should be:
1. $$12$$ m/s
2. $$13$$ m/s
3. $$5$$ m/s
4. $$10$$ m/s

Subtopic: Â Relative Motion |
Â 69%
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