$A$ police van moving on a highway with a speed of $30\; km/h$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192\; km/h.$ If the muzzle speed of the bullet is $150\; m/s,$ with what speed (in $m/s$) does the bullet hit the thief's car?

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is:

$A$ car with a vertical windshield moves in a rainstorm at a speed of $40 \, km/h$. The raindrops fall vertically with a constant speed of $20 \, m/s$. The angle at which the raindrops strike the windshield is .........

Two boys are standing at points $A$ and $B$ on the ground,where distance $AB = x$. The boy at $B$ starts running perpendicular to $AB$ with velocity $v_1$. The boy at $A$ starts running simultaneously with velocity $v$ and meets the other boy in time $t$. The value of $t$ is:

On a long horizontally moving belt,a child runs to and fro with a speed $9 \, km \, h^{-1}$ (with respect to the belt) between his father and mother located $50 \, m$ apart on the moving belt. The belt moves with a speed of $4 \, km \, h^{-1}$. For an observer on a stationary platform,the speed of the child running in the direction of motion of the belt is ..... $km \, h^{-1}$.

$A$ bird is flying to and fro between two cars moving towards each other on a straight road. One car has a speed of $18 \,km/h$ while the other has a speed of $27 \,km/h$. The bird starts moving from the first car towards the second car with a speed of $36 \,km/h$ when the two cars are separated by $36 \,km$. What is the total distance covered by the bird?