Relative Motion: Rain Example

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.

1. 

2. 

3. 

4. 

Q. An aero plane is flying horizontally with a constant velocity of 100 km $p{h}^{-1}$ at a height of 1 km from the ground level. At
t = 0, it start dropping packets at constant time interval of $I_0$. If R represents the separation between two consecutive points of impact on the ground then for the first 3 packets$R_1:R_2$ is

1. 1 : 1
2. 2 : 1
3. 1 : 2
4. 1 : 3

Q. Rain is falling vertically with a speed of 30 m s¯¹. A woman rides a bicycle with a speed of 10 m s¯¹ in the north to south direction. What is the direction in which she should hold her umbrella ?

Q.

A swimmer can swim in still water at $ 1.5 m{s}^{-1}$. The river is flowing with $ 2 m{s}^{-1}$ from left to right. The minimum time taken by swimmer to cross the river and the drift in that case are respectively

1 iver flow V=2ms d =200m 

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

1. $3\text{km/h}$
2. $3\sqrt{2}\text{km/h}$
3. $2\sqrt{3}\text{km/h}$
4. $\frac{3}{2}\text{km/h}$

Q. A man walks at the rate of $3\text{km/hr}$. Rain appears to him falling in vertical direction at the rate of $3\sqrt{3}\text{km/hr}$. Which of the following options is correct regarding the actual velocity of rain?

1. $6\text{km/hr}$, inclined at an angle of ${30}^{\circ }$ to the vertical towards the man's motion.
2. $3\text{km/hr}$, inclined at an angle of ${30}^{\circ }$ to the vertical towards the man's motion.
3. $6\text{km/hr}$, inclined at an angle of ${45}^{\circ }$ to the vertical towards the man's motion.
4. $6\text{km/hr}$, inclined at an angle of ${60}^{\circ }$ to the vertical towards the man's motion.

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. When a man moves down an inclined plane with a constant speed $5\text{m/s}$ which makes an angle of ${37}^{\circ }$ with the horizontal, he finds that the rain is falling vertically downwards. When he moves up the same inclined plane with the same speed, he finds that the rain makes an angle $\theta ={\tan }^{-1}\left(\frac{7}{8}\right)$ with the horizontal. The speed of the rain with respect to the ground is

1. $\sqrt{116}\text{m/s}$
2. $\sqrt{32}\text{m/s}$
3. $\sqrt{10}\text{m/s}$
4. $5\text{m/s}$

Q. A man moving with velocity $5\text{m/s}$ along a straight line observes rain falling vertically at the rate of $10\text{m/s}$. Find the speed of rain with respect to ground, and angle$\left(\theta \right)$ made from vertical by the rain as seen from ground.

1. $5\sqrt{5}\text{m/s},\theta =\frac{{\tan }^{-1}4}{2}$
2. $5\sqrt{5}\text{m/s},\theta ={\tan }^{-1}\frac{1}{2}$
3. $10\text{m/s},\theta ={\tan }^{-1}2$
4. $10\text{m/s},\theta ={\tan }^{-1}\frac{1}{2}$

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. 800 m

2. 200 m

3. 500 m

4. 400 m

Q. Rain appears to fall vertically downwards to a man walking at the rate of $3\text{km/h}$. When he increases his speed to $6\text{km/h}$, the rain appears coming to him at an angle of ${45}^{\circ }$ with the vertical. The speed of rain is

1. $3\sqrt{3}\text{km/h}$
2. $3\sqrt{2}\text{km/h}$
3. $3\sqrt{5}\text{km/h}$
4. $5\sqrt{3}\text{km/h}$

Q. A person standing on a road has to hold his umbrella at 60${}^{\circ }$ with the vertical to keep away rain. He throws the umbrella and starts running in horizontal direction at a speed of $20\text{m/s}$. He finds that the rain drops are hitting his head vertically. Find the speed of rain drops with respect to ground.

1. $\frac{40}{\sqrt{3}}\text{m/s}$
2. $11.5\text{m/s}$
3. $\frac{20}{\sqrt{3}}\text{m/s}$
4. $17\text{m/s}$

Q. Rain is falling vertically downwards with a velocity of $4km/h$. A man walks in the rain with a velocity of $3km/h$. The raindrops will fall on the man with a velocity of magnitude

1. $1km/h$
2. $3km/h$
3. $4km/h$
4. $5km/h$

Q. A man standing on a road has to hold his umbrella at ${60}^o$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\sqrt{3}km/h$. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to the ground.

1. $5km/h$
2. $10km/h$
3. $10\sqrt{2}km/h$
4. $20km/h$

Q. Rain is falling downwards with a velocity of $3\text{km/h}$. A man walks in the rain with a velocity of $4\text{km/h}$. Raindrops will appear to be falling on the man with a velocity of

1. $1\text{km/h}$
2. $3\text{km/h}$
3. $4\text{km/h}$
4. $5\text{km/h}$

Q. Rain is falling vertically with a speed of $30m/s$. A woman rides a bicycle with a speed of $12m/s$ in east to west direction. What is the direction in which she should hold her umbrella?

1. At an angle of ${\tan }^{-1}(\frac{2}{5})$ with the vertical towards the east
2. At an angle of ${\tan }^{-1}(\frac{2}{5})$ with the vertical towards the west
3. At an angle of ${\tan }^{-1}(\frac{5}{2})$ with the vertical towards the east
4. At an angle of ${\tan }^{-1}(\frac{5}{2})$ with the vertical towards the west

Q. A man holds an umbrella at ${30}^{\circ }$ with the vertical to keep himself dry. He then runs at a speed of $10\text{m/s}$ and finds the rain drops to be hitting vertically. Speed of the rain drops w.r.t the running man and w.r.t earth are

1. $20\text{m/s}$, $10\text{m/s}$
2. $10\text{m/s}$, $20\sqrt{3}\text{m/s}$
3. $10\sqrt{3}\text{m/s}$, $20\text{m/s}$
4. $20\text{m/s}$, $10\sqrt{3}\text{m/s}$

Q. A man standing on a road has to hold his umbrella at ${30}^{\circ }$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10km/h$. He finds that raindrops are hitting his head vertically. Find the speed of raindrops with respect to the ground.

1. $5km/h$
2. $10km/h$
3. $10\sqrt{2}km/h$
4. $20km/h$

Q. A man walks at the rate of $3\text{km/hr}$. Rain appears to him falling in vertical direction at the rate of $3\sqrt{3}\text{km/hr}$. Which of the following options is correct regarding the actual velocity of rain?

1. $6\text{km/hr}$, inclined at an angle of ${30}^{\circ }$ to the vertical towards the man's motion.
2. $3\text{km/hr}$, inclined at an angle of ${30}^{\circ }$ to the vertical towards the man's motion.
3. $6\text{km/hr}$, inclined at an angle of ${45}^{\circ }$ to the vertical towards the man's motion.
4. $6\text{km/hr}$, inclined at an angle of ${60}^{\circ }$ to the vertical towards the man's motion.

Q. A man is coming down an inclined plane of angle ${30}^{\circ }$ with speed $2\sqrt{3}\text{m/s}$. He has to keep his umbrella vertical to protect himself from rain. If the actual magnitude of velocity of rain is $5\text{m/s}$, at what angle with vertical should he keep his umbrella when he is at rest?

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${37}^{\circ }$
4. ${53}^{\circ }$

Q. A stationary person observes that rain is falling vertically down at $30km/hr$. A cyclist is moving up on an inclined plane making an angle ${30}^{\circ }$ with horizontal at $10km/hr$. At what angle with the inclined plane the cyclist should hold his umbrella to protect himself from rain?

1. ${\tan }^{-1}\left(\frac{3\sqrt{3}}{5}\right)$
2. ${\tan }^{-1}\left(\frac{\sqrt{3}}{7}\right)$
3. ${\tan }^{-1}\left(\frac{3}{5}\right)$
4. ${\tan }^{-1}\left(\frac{3\sqrt{3}}{7}\right)$

Q. A man standing on a road has to hold his umbrella at ${30}^{\circ }$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10{\text{kmh}}^{-1}$ . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

1. $20{\text{kmh}}^{-1}$
2. $10\sqrt{2}{\text{kmh}}^{-1}$
3. $20\sqrt{3}{\text{kmh}}^{-1}$
4. $10{\text{kmh}}^{-1}$

Q. Rain is falling vertically with a speed of $12\sqrt{3}m/s$. A woman rides a bicycle with a speed of $12m/s$ from East to West direction. What is the velocity of rain relative to the woman?
(Take east and vertically upward as positive x-axis and positive y-axis respectively.)

1. $(12\sqrt{3}\hat{i}+12\hat{j})m/s$
2. $(12\sqrt{3}\hat{i}+12\sqrt{3}\hat{j})m/s$
3. $(12\hat{i}-12\sqrt{3}\hat{j})m/s$
4. $(-12\hat{i}-12\sqrt{3}\hat{j})m/s$

Q. A man running on a horizontal road at $8{\text{ms}}^{-1}$ finds rain falling vertically. If he increases his speed to $12{\text{ms}}^{-1}$, he finds that drops make ${30}^{\circ }$ angle with the vertical. Find the velocity of rain with respect to the road.

1. $4\sqrt{7}{\text{ms}}^{-1}$
2. $8\sqrt{2}{\text{ms}}^{-1}$
3. $7\sqrt{3}{\text{ms}}^{-1}$
4. $8{\text{ms}}^{-1}$

Q. It is raining vertically with a velocity of $25{\text{ms}}^{-1}$. A woman rides a bicycle with a speed of $10{\text{ms}}^{-1}$ in north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to save herself from the rain?

1. ${\tan }^{-1}\left(0.4\right)$
2. ${\tan }^{-1}\left(1\right)$
3. ${\tan }^{-1}\left(\sqrt{3}\right)$
4. ${\tan }^{-1}\left(2.6\right)$

Q. A man standing on a road has to hold his umbrella at ${60}^{\circ }$ with the horizontal to keep the rain away. He throws the umbrella and starts running at $20km{h}^{-1}$ . He finds that raindrops are hitting his head vertically. The actual speed of raindrops is

1. $20km{h}^{-1}$
2. $30km{h}^{-1}$
3. $40km{h}^{-1}$
4. $15km{h}^{-1}$

Q. A car is moving in a rainstorm at a speed of $36\text{km/hr}$. The rain drops fall vertically w.r.t the ground with a constant speed of $20\text{m/s}$. The speed of the raindrops w.r.t the car is

1. $10\sqrt{5}\text{m/s}$
2. $50\sqrt{5}\text{m/s}$
3. $10\sqrt{2}0\text{m/s}$
4. $5\sqrt{5}\text{m/s}$

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)

1. $0^{\circ }$

2. ${30}^{\circ }$

3. ${45}^{\circ }$

4. ${60}^{\circ }$

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. 400 m

2. 800 m

3. 200 m

4. 500 m

Q. Rain is falling vertically with $3{\text{ms}}^{-1}$ and a man is moving due North with $4{\text{ms}}^{-1}$. In which direction he should hold the umbrella to protect himself from rains?

1. ${37}^{\circ }$ North of vertical
2. ${30}^{\circ }$ South of vertical
3. ${53}^{\circ }$ North of vertical
4. ${60}^{\circ }$ South of vertical