$A$ body starts from rest from the origin with an acceleration of $6\,m/s^2$ along the $x$-axis and $8\,m/s^2$ along the $y$-axis. Its distance from the origin after $4\,s$ will be........$m$

Two projectiles $A$ and $B$ are thrown with the same speed such that $A$ makes an angle $\theta$ with the horizontal and $B$ makes an angle $\theta$ with the vertical. Then:

$A$ boy throws a ball with a velocity $V_0$ at an angle $\alpha$ to the ground. At the same time,he starts running with a uniform velocity to catch the ball before it hits the ground. To achieve this,he should run with a velocity of

$A$ 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 moves towards east with velocity $5\, m/s$. After $10\, s$,its direction changes towards north with the same velocity. The average acceleration of the particle is

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: