Four persons $K, L, M$ and $N$ are initially at the corners of a square of side length $d$. If every person starts moving with speed $v$ such that $K$ is always headed towards $L$,$L$ towards $M$,$M$ towards $N$,and $N$ towards $K$,then the four persons will meet after

$A$ projectile is launched at an angle $\alpha$ with the horizontal with a velocity $20 \; m/s$. After $10 \; s$,its inclination with the horizontal is $\beta$. The value of $\tan \beta$ will be: $(g = 10 \; m/s^2)$

$A$ body of mass $1 \, kg$ starts moving from rest at $t = 0$ in a circular path of radius $8 \, m$. Its kinetic energy varies as a function of time as: $K.E. = 2t^2 \, J$,where $t$ is in seconds. Then:

Two particles having mass $M$ and $m$ are moving in a circular path having radius $R$ and $r$. If their time periods are the same,then the ratio of their angular velocities will be:

$A$ projectile is fired at an angle of $45^o$ with an initial kinetic energy $K$. What is the kinetic energy of the projectile at its maximum height?

State whether the following statements are true or false:
$(a)$ If the angular velocity is constant on a circular path,the linear velocity is also constant.
$(b)$ In projectile motion,the velocity vector of the projectile is always perpendicular to the acceleration vector.
$(c)$ For the maximum horizontal range $R$ of a projectile,the maximum height attained is $\frac{R}{4}$.
$(d)$ If $|\vec{A} \times \vec{B}| = AB$,then the angle between $\vec{A}$ and $\vec{B}$ is zero.