A man desires to swim across a river through shortest distance the velocity of river water is $3\,Km\,{h^{ - 1}}$. He can swim in still water at $6Km\,{h^{ - 1}}$. At what angle with the velocity of flow of river should he swim?

The time of flight of a projectile on an upward inclined plane depends upon

The acceleration experienced by a moving boat after is engine is cut-off, is given by $a = - k{v^3},$, where k is a constant. If ${v_0}$ is the magnitude of velocity at cut-off, then the magnitude of the velocity at time t after the cut off is

Two bodies are projected from the same point with equal speeds in such directions that they both strike the same point on a plane whose inclination is $\beta$. If $\alpha$ be the angle of projection of the first body with the horizontal the ratio of their times of flight is

Neglecting the air resistance, the time of flight of a projectile is determined by

Two bodies are projected from roof with same speed in different directions. If air resistance is not taken into account then

When an object is shot from the bottom of a long smooth inclined plane kept at an angle ${60^{\rm{o}}}$ with horizontal, it can travel a distance ${x_1}$ along the plane. But when the inclination is decreased to ${30^{\rm{o}}}$ and the same object is shot with the velocity, it can travel ${x_2}$ distance. Then ${x_1}:{x_2}$ will be:

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south

Two bodies are projected from the same point with equal speeds in such directions that they both strike the same point on a plane whose inclination is $\beta$. If $\alpha$ be the angle of projection of the first body with the horizontal the ratio of their times of flight is

A stone is projected from the ground with velocity $50{\rm{\;m}}{{\rm{s}}^{ - 1}}$ and angle of ${30^0}$. It crosses a wall after 3 s. How far beyond the wall the stone will strike the ground?

A particle is projected at an angle of ${60^0}$ above the horizontal with a speed of $10{\rm{\;m}}{{\rm{s}}^{ - 1}}$. After some time the direction of its velocity makes an angle of ${30^0}$ above the horizontal. The speed of the particle at this instant is