Relative Velocity

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.

Explain the concept of the relative velocity. Draw position-time graphs of two objects moving along a straight line when their relative velocity is (i) zero and (ii) non-zero.

Derive the second and third equations of motion by calculus method.

A car moving on a straight line covers a distance at speed $\mathrm{v}$ and the return journey with a speed of $2\mathrm{v}$ Find (i) average speed and (ii) mean speed.

Two trains$\mathrm{A} \mathrm{and} \mathrm{B}$ of length $350\mathrm{m}$ each are moving on two parallel tracks with equal velocities of $100 \mathrm{km}/\mathrm{hr}$ in the same direction, $A$

ahead of $B$. The driver of $B$desires to overtake $\mathrm{A}$.and accelerates by $1 {\mathrm{ms}}^{-2.}$. If after $50 \sec .$ The guard of $B$ just brushes past the driver of $A$, then the original distance between the guard of $\text{B}$ and the driver of $\mathrm{A}$ is :

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.

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

A lift in which a man is standing, is moving upward with a speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ The man drops a coin from a height of $4.9 \mathrm{m}$ and if $g=9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$, then the coin reaches the floor of the lift after a time of $1 \mathrm{s}$.

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 body can be at rest and in motion at the same time.

Rest is a relative term.

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  $g=9.8m{s}^{-2}$]

To find the speed of a river's current, a boatman decides to carry out the following experiment. He drops a wooden bar into the water and he sets off downstream, rowing along the flow of river. After $40 \min$, he reaches point $A$, $1 \mathrm{km}$ from his starting point, and turns back. After travelling some distance upstream, he picks up the bar then quickly turns around again and, rowing downstream once more, reaches $A$ for the second time $24 \min$ after picking the bar. Assuming that the speeds of both current and the boat relative to water are constant, what is the speed of the current?