The equation of a projectile is $y=\sqrt{3} x-\frac{ x^2}{2}$, the velocity of projection is

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?

A body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of ${30^o}$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

A ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^o$ with the horizontal. At the highest point, the ratio of their potential energies is

Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to  horizontal, after one more second it is travelling horizontally. What is the magnitude and  direction of its velocity at initial point