A ball is thrown at an angle $\theta$ with the horizontal. Its horizontal range is equal to its maximum height. This is possible only when the value of $\tan \theta$ is ..........

A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following remains constant

A grasshopper can jump maximum distance $1.6\; m$. It negligible time of the ground. How far can it go in $10 \;s$?

Two particles $A$ and $B$ are projected simultaneously from a fixed point of the ground. Particle $A$ is projected on a smooth horizontal surface with speed $v$, while particle $B$ is projected in air with speed $\frac{2 v}{\sqrt{3}}$. If particle $B$ hits the particle $A$, the angle of projection of $B$ with the vertical is

A boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant he starts running with uniform velocity to catch the ball before if hits the ground. To achieve this he should run with a velocity of

A particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v (t)$ is depicted by which of the following curves?