Relative Motion: Rain Example

Q. 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 $10\text{km/hr}$. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be

1. $10\text{km/hr}$
2. $20\text{km/hr}$
3. $30\text{km/hr}$
4. $40\text{km/hr}$

Q. A man sitting in a bus travelling in a direction from west to east with a speed of 40 km/h observes that the rain-drops are falling vertically down. To the another man standing on ground the rain will appear

1. To fall at an angle going from east to west
2. The information given is insufficient to decide the direction of rain.
3. To fall vertically down
4. To fall at an angle going from west to east

Q.

A man is coming down an incline of angle ${30}^{\circ }$. When he walks with speed $\sqrt{3}$m/s he has to keep his umbrella vertical w.r.t. ground to protect himself from rain. The actual speed of rain is 5 m/s. At what angle with vertical should he keep his umbrella when he is at rest so that he does not get drenched?

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Q.

Rain is falling vertically with a speed of $12m{s}^{-1}$.A cyclist is moving east to west with a speed of $12\sqrt{3}m{s}^{-1}$.In order to protect himself from rain at what angle he should hold his umbrella w.r.t vertical.

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Q.

A, B, C, D are four trees, located at the vertices of a square. Wind blows from A to B with uniform speed. The ratio of times of flight of a bird from A to B and from B to A is 'n'. At what angle should the bird fly from the direction of wind flow, in order that it starts from A and reaches C.Let

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Q.

Consider the situation given in the diagram two cars are moving along road 1 and road 2. Draw the direction of the motion of car B as seen from car A

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Q.

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. How far south of his starting point will be reach the bank?

1. 200 m

2. 400 m

3. 800 m

4. 500 m

Q.

A flag is hoisted on the steamer boat.On the basis of the data given below find out the direction of flutter of

the flag

${\overrightarrow{v}}_{steamer/water}=10\sqrt{3}m{s}^{-1}$ towards North

${\overrightarrow{v}}_{water}=5m{s}^{-1}$ towards East

${\overrightarrow{v}}_{wind}=5m{s}^{-1}$ towards East

(Assume the wind does not affect the steamer)

1. North

2. South

3. East

4. West

Q.

From the previous problem at what angle to the horizontal must be steered in order to reach a point on the opposite bank directly east from the starting point? (Assuming his speed w.r.t. to the river is 4 m/s)

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Q.

A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes $10\text{minutes}$ with a drift of $120\text{m}$. If he crosses the river taking the shortest route, he takes $12.5\text{minutes}$, find the velocity of the boat with respect to water.

1. $12\text{m/min}$

2. $20\text{m/min}$

3. $5\text{m/min}$

4. $31\text{m/min}$