$A$ sportsman runs around a circular track of radius $r$ such that he traverses the path $ABAB$. The distance travelled and displacement,respectively,are

At $t = 0$,a projectile is fired from a point $O$ (taken as origin) on the ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It passes through two points $A$ and $B$,each at a height of $75 \, m$ above the horizontal,as shown in the figure. Find the distance (in meters) of the particle from the origin at $t = 2 \, s$.

Twelve persons are initially at $12$ corners of a regular polygon of $12$ sides of side length $a$. Each person moves with a uniform speed $v$ in such a manner that person $1$ is always directed towards person $2$,person $2$ towards person $3$,person $3$ towards person $4$,and so on. The time after which they meet is

In the projectile motion of an object,the object reaches its maximum height where its speed is half of its initial speed. Then the ratio between the range and the maximum height of the projectile is

$A$ man standing on the roof of a house of height $h$ throws one particle vertically downwards and another particle horizontally with the same velocity $u$. The ratio of their velocities when they reach the earth's surface will be

The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be: