Relative Velocity in Two Dimensions

A boat whose speed in the still water is $16 \mathrm{kmph}$ covers a distance of $30 \mathrm{km}$ up stream and returns taking $4 \mathrm{hrs}$ in total. What is the speed of the current?

The wind is blowing from the south at $10 \mathrm{m}/\mathrm{s}$but to a cyclist, it appears blowing from the east at $10 \mathrm{m}/\mathrm{s}$. The velocity of the cyclist is 

On a rainy day, the rain was falling vertically with a speed of $15 m{s}^{-1}$. A wind started blowing, with a speed of $5m{s}^{-1}$ from north to south. In which direction should a girl waiting at a bus stop hold her umbrella?

A train is accelerating towards north at the rate of $4.9 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$. Find the acceleration of a bolt which falls from the ceiling relative to  the Earth?

A ship is steaming north at $8\sqrt{3} \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$ and a man walks across its deck in a direction due west at $8 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$. Find his resultant velocity in the ship.

To a man walking at the rate of $2 \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$h$}\right.$, rain appears to fall vertically. When he doubles his speed, it appears to fall at $30°$ to the vertical. Find real speed and direction of rain.

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 the ground. Calculate the relative velocity of the boat with respect to water.

A cat is climbing a vertical pole with a speed of $4 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ and a dog is running towards the pole with a speed of $8 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. What is the velocity of the dog relative to the cat ?

The wind is blowing from the south at $10 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$, but to a cyclist it appears to be blowing from the east at $10 \raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. Determine the velocity of the cyclist in vector form.

What is relative velocity ? Write down the equation for the velocity of one body with respect to
another ?

Derive an expression for the relative velocity of a body $A$ with respect to another body $B$ moving in different directions.

Explain relative velocity in two dimensional motion.

A river flows with a speed more than the maximum speed with which a person can swim in still water. He intends to cross the river by the shortest possible path, (i.e., he wants to reach the point on the opposite bank which directly opposite to the starting point). Which of the following is correct?

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

A boat can travel with a speed of $13 \mathrm{km} {\mathrm{hr}}^{-1}$ in still water. If the speed of the stream is $4 \mathrm{km} {\mathrm{hr}}^{-1}$. Find the time taken by the boat to go $81 \mathrm{km}$ upstream?

The speed of a motorboat in still water $20 \mathrm{km} {\mathrm{hr}}^{-1}$ And river flow is $5 \mathrm{km} {\mathrm{hr}}^{-1}$. A float is dropped from the boat when it starts moving upstream. After moving $1.5 \mathrm{km}$ The boat returns. The boat will catch the float (from initial instant) after;

Describe the appearance of Rain Drop in Presence of Wind.

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 ?

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 resultant velocity of 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?