Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown,the relative velocities of $A$ with respect to $B, C$ and $D$ are in the directions:

Derive the expressions for the time taken to reach maximum height,the total time of flight,and the maximum height attained by a projectile.

$A$ particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^2Rt^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it,is

$A$ particle moves in the $xy$-plane with velocity $v_x = 8t - 2$ and $v_y = 2$. If it passes through the point $(14, 4)$ at $t = 2 \, s$,the equation of its path is:

Two bodies were thrown simultaneously from the origin: one straight up and the other at an angle of $60^{\circ}$ to the vertical. The initial velocity of each body is $10 \ m \ s^{-1}$. Neglecting air resistance, the distance between the two bodies after $t=2 \ s$ is (Use $g=10 \ m \ s^{-2}$):

$A$ particle is moving in $x-y$ plane according to $\vec{r} = b \cos \omega t \hat{i} + b \sin \omega t \hat{j}$, where $\omega$ is a constant. Which of the following statement$(s)$ is/are true?