The width of river is $1\; km$. The velocity of boat is $5\; km/hr$. The boat covered the width of river with shortest will possible path in $15 \;min$. Then the velocity of river stream is

Two particles $A$ and $B$ start moving with velocities $20 \,m / s$ and $30 \sqrt{2} \,m / s$ along $x$-axis and at an angle $45^{\circ}$ with $x$-axis respectively in $x y$-plane from origin. The relative velocity of $B$ w.r.t. $A$ is ........... $m / s$

Wind is blowing in the north direction at speed of $2 \,\,m/s$ which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him :

A river is flowing from west to east at a speed of $8\,m$ per min. A man on the south bank of the river, capable of swimming at $20\,m / min$ in still water, wants to swim across the river in the shortest time. He should swim in a direction

A boat crosses a river with a velocity of $8\, km/h$. If the resulting velocity of boat is $10 \,km/h $ then the velocity of river water is...........$km/h$

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v,$ he sees that rain drops are coming at an angle $60^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1+\beta) v ,$ this angle changes to $45^{\circ} .$ The value of $\beta$ is close to$......$