$A$ boy standing on the footpath tosses a ball straight up and catches it. The driver of a car passing by,moving with uniform velocity,sees this. The trajectory of the ball as seen by the driver will be:

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:

$A$ river is flowing with a velocity of $5 \ km/hr$ as shown in the figure. $A$ boat starts from $A$ and reaches the other bank. The width of the river is $b = 300 \ m$. The velocity of the boat in still water is $v_{br} = 3 \ km/hr$. If the boat aims to reach the point directly opposite to $A$ (point $B$),but due to the river flow,it reaches point $C$,what is the distance $AC$ covered by the boat? (Note: The boat is steered such that it maintains a straight path relative to the ground).

Two cars, at a certain instant, are $50 \ km$ apart on a line running from south to north. The one farther north is moving west at $25 \ km/hr$. The other is moving towards north at $25 \ km/hr$. How long do they take to reach their distance of closest approach (in $min$)?

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54\; km\; h^{-1},$ and train $B$ moves south with a speed of $90\; km\; h^{-1}.$ What is the velocity (in $m\; s^{-1}$) of a monkey running on the roof of the train $A$ against its motion (with a velocity of $18\; km\; h^{-1}$ with respect to the train $A$) as observed by a man standing on the ground?

Two cars $A$ and $B$ are moving with speeds $v_A = 120 \text{ km/h}$ and $v_B = 50 \text{ km/h}$ respectively in the directions as indicated by the arrows in the figure below. What is the relative speed of car $B$ with respect to car $A$ (in $\text{ km/h}$)?