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?

A particle is projected with speed v at an angle {\rm{heta }}\left( {0 < heta < \frac{{\rm{\pi }}}{2}} \right) above the horizontal from a height H above the ground. If v= speed with which particle hits the ground and t=time taken by particle to reach ground, then

A particle is projected with a velocity such that its range on the horizontal plane is twice the greatest height attained by it, The range of the projectile is (when it is acceleration due to gravity is’g’)

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

A boat crosses a river from port A to port B, which are just on the opposite side. The speed of the water is ${V_W}$ and that of boat is ${V_B}$ relative to still water. Assume ${V_B} = 2{V_W}$. What is the time taken by the boat, if It has to cross the river directly on the AB line

A boy playing on the roof of a 10 m high building throws a ball with a speed of $10\;{\rm{m}}{{\rm{s}}^{ - 1}}$ at an angle of ${30^0}$ with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? (g = 10{\rm{\;m}}{{\rm{s}}^{ - 2}},\sin 30^\circ  = 1/2,{\rm{\;cos\;}}30^\circ  = \sqrt 3 /2)

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip is

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip is

The potential energy of a projectile at its maximum height is equal to its kinetic energy there. If the velocity of projection is $20\,m{s^{ - 1}}$ its time of flight is $\left( {g = 10\,\,m{s^{ - 2}}} \right)$

A ball is projected with kinetic energy E. at an angle of ${45^0}$ to the horizontal. At the highest point during its flight, its kinetic energy will be

A body is projected from the earth at angle ${30^0}$ with the horizontal with some initial velocity. If its range is 20 m, the maximum height reached by its is (in metre )