Relative Velocity in Two Dimensions

Raindrops are falling vertically with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. To a cyclist moving on a straight road, the raindrops appear to be coming with a velocity of $20 \mathrm{m} {\mathrm{s}}^{-1}$. The velocity of the cyclist is

Raindrops are falling vertically downwards at $2m s{ }^{-1}$. Then the wind starts blowing from north to south at $1.5\mathrm{m} {\mathrm{s}}^{-1}$. Find the angle at which a man should hold the umbrella to protect himself from the rain ?

A boat is moving $2 km$ against the current of the stream in $1 hour$ and moves $1 km$ in the direction of the current in $10 minutes$. How long (in minutes) will it take the boat to go $5 km$ in stationary water?

A river is flowing with a speed of $3 \mathrm{m} {\mathrm{s}}^{-1}$.  A boatman reaches a point while travelling upstream in $30 \min$ and comes back to the initial point in $15 \min$ following the same path. Find the total distance covered by him.

A shower of rain appears to fall vertically downwards with a velocity $4 \mathrm{km}/\mathrm{h}$on a person walking westwards with a velocity of $3 \mathrm{km}/\mathrm{h}$Calculate the actual velocity of the rain 

A person standing on the road has to hold his umbrella at $60°$ with the vertical. He throws the umbrella and starts running at $20 m{s}^{-1}$. He finds that the raindrops are hitting his head vertically. Find the speed of the raindrop with respect to the road and the moving person.

A plane is travelling eastward at a speed of $500\mathrm{}\mathrm{k}\mathrm{m}\mathrm{}{\mathrm{h}}^{-1}$. But a $90\mathrm{}\mathrm{k}\mathrm{m}\mathrm{}{\mathrm{h}}^{-1}$ wind is blowing southward. What is the speed of the plane relative to the ground?

A boy is moving due east with a velocity of $50\mathrm{}\mathrm{m}{\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$. The rain is falling vertically with a velocity of $250\mathrm{}\mathrm{m}\mathrm{}{\mathrm{m}\mathrm{i}\mathrm{n}}^{-1}$. Atwhat angle and with what velocity rain appears to fall to the boy?

To a person moving eastwards with a velocity $4.8\mathrm{}\mathrm{k}\mathrm{m}\mathrm{}{\mathrm{h}}^{-1}$,rain appears to fall vertically downwards with a speed of $6.4\mathrm{}\mathrm{k}\mathrm{m}\mathrm{}{\mathrm{h}}^{-1}$. What is the actual speed and direction of rain?

A cyclist is moving due east with a velocity of $10\mathrm{}\mathrm{k}\mathrm{m}\mathrm{}{\mathrm{h}}^{-1}$.There is no wind and rain appears to fall at an angle of $10°$ to the vertical. Calculate the actual speed of the rain.

Rain, driven by the wind, falls on a railway compartment with velocity of 20 m/s, at an angle of 30^o to the vertical. The train moves, along the direction of wind flow, at a speed of 108 km/hr. Determine the apparent velocity of rain for a person sitting in the train.

A ball is dropped from a height of $49 m$. The wind is blowing horizontally. Due to wind, a constant horizontal acceleration is provided to the ball. Choose the correct statement (s). [Take  $g=9.8m{s}^{-2}$]

A jet airplane travelling at the speed of $500\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ ejects its products of combustion at the speed of $1500\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ relative to the jet plane. The speed of the products of combustion with respect to an observer on the ground is

Two particles are projected simultaneously in the same vertical plane, from the same point, both with different speeds and at different angles with horizontal. The path followed by one, as seen by the other, is –

Rain is falling vertically with a speed of $30 \mathrm{m} {\mathrm{s}}^{-1}$. A woman rides a bicycle with a speed of $12 \mathrm{m} {\mathrm{s}}^{-1}$ in east to west direction. In which direction she should hold her umbrella?

Rain is falling vertically with a speed of $35 \mathrm{m} {\mathrm{s}}^{-1}$. Winds start blowing after some time with a speed of $12 \mathrm{m} {\mathrm{s}}^{-1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop, hold his umbrella to protect himself from rain?

A boat which has a speed of $5 \mathrm{km} {\mathrm{hr}}^{-1}$in still water crosses a river of width $1 \mathrm{km}$ along the shortest possible path in $15 \min$. The velocity of the river water in $\mathrm{km} {\mathrm{hr}}^{-1}$ is

Some persons hire a boat for $4$ hours. The river flows at a speed of $5 \mathrm{km} {\mathrm{h}}^{-1}$ and the boat moves with speed of $15 \mathrm{km} {\mathrm{h}}^{-1}$ relative to the water. How far along the flow direction, they can go if they have to return in $4 \mathrm{hr}$?

The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is :

(a) 2 km/hr

(b) 2.5 km/hr

(c) 3 km/hr

(d) 4 km/hr

A motorboat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is: