Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^{\circ}$ and $60^{\circ}$ with respect to the horizontal respectively as shown in figure . The speed of $A$ is $100 \sqrt{3} ms ^{-1}$. At time $t=0$, an observer in A finds $B$ at a distance of $500 \ m$. This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A$. If at $t = t _0$, $A$ just escapes being hit by $B , t _0$ in seconds is:

Thief's car is moving with a speed of $10\,m/s$. A police van chasing this car with a speed of $5\,m/s$ fires a bullet at the thief's car with muzzle velocity $72\,km/h$. Find the speed with which the bullet with hit the car.............$m/s$

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a$. If $\alpha$ is the angle between the lines of motion of two particles, then the least value of relative velocity will be at time given by

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 :

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

A boat is moving with a velocity $3i + 4j $ with respect to ground. The water in the river is moving with a velocity $-3i -4j $ with respect to ground. The relative velocity of the boat with respect to water is