If two bodies $A$ and $B$ are projected with the same velocity $u$ but with different angles $\theta_1$ and $\theta_2$ respectively with the horizontal such that both have the same range,then the ratio of the times of flight of the bodies $A$ and $B$ is:

$A$ stone thrown with velocity $u$ at angles $\theta$ and $(90^{\circ}-\theta)$ with the horizontal reaches maximum heights $H_1$ and $H_2$ respectively. Its horizontal range is

$A$ car runs at a constant speed on a circular track of radius $100\,m$,taking $62.8\,s$ for every circular lap. The average velocity and average speed for each circular lap respectively are:

$A$ fighter plane flying horizontally at an altitude of $1.5 \; km$ with a speed of $720 \; km/h$ passes directly overhead an anti-aircraft gun. At what angle from the vertical should the gun be fired for the shell with a muzzle speed of $600 \; m s^{-1}$ to hit the plane? At what minimum altitude should the pilot fly the plane to avoid being hit? (Take $g = 10 \; m s^{-2}$).

$A$ particle $A$ moves along the line $y=30 \ m$ with a constant velocity $v$ parallel to the $x$-axis. At the moment particle $A$ passes the $y$-axis, a particle $B$ starts from the origin with zero initial speed and a constant acceleration $a=0.40 \ m/s^2$. The angle between $a$ and the $y$-axis is $60^{\circ}$. If the particles $A$ and $B$ collide after some time, then the value of $|v|$ will be (in $m/s$)

$A$ particle moving in the $xy$ plane experiences a velocity-dependent force $\overrightarrow{F} = k(v_y \hat{i} + v_x \hat{j})$,where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\overrightarrow{v}$. If $\overrightarrow{a}$ is the acceleration of the particle,then which of the following statements is true for the particle?