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

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. ${45}^{\mathrm{o}}$ 

2. 30^o

3. 60^o 

4. 90^o

A boat is moving with a velocity 3i + 4j with respect to ground. The water in the river is moving with a velocity – 3i – 4j with respect to ground. The relative velocity of the boat with respect to water is 

1. 8j

2. – 6i – 8j

3. 6i +8j

4. $5\sqrt{2}$

Raindrops are falling with a 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. $\sqrt{\frac{{\mathrm{v}}^2 + {\mathrm{u}}^2}{2}}$

4. $\sqrt{{\mathrm{v}}^2 + {\mathrm{u}}^2}$

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 $120°$ 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

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.  $\frac{4}{3}$

A man standing on a road holds his umbrella at 30° 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

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. 1/8 h

2. 1/4 h

3. 1/2 h

4. 1 h

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

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