$A$ boy throws a cricket ball from the boundary to the wicket-keeper. If the frictional force due to air cannot be ignored,the forces acting on the ball at the position $X$ are represented by

$A$ 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

$A$ particle is moving such that its position coordinates $(x, y)$ are $(2 \, m, 3 \, m)$ at time $t = 0$,$(6 \, m, 7 \, m)$ at time $t = 2 \, s$,and $(13 \, m, 14 \, m)$ at $t = 5 \, s$. The average velocity vector $\vec{v}_{av}$ from $t = 0$ to $t = 5 \, s$ is:

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. The horizontal separation between the points $A$ and $B$ is . . . . . . $m$.

$A$ small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track,the normal reaction is maximum in

When a body moves with a constant speed along a circle,