The greatest height to which a man can throw a stone is $h$. The greatest distance to which he can throw it will be:

$A$ particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is ($g=$ acceleration due to gravity).

If a particle of mass $m$ covers half of the horizontal circle with constant speed $v$,then the change in its kinetic energy is

$A$ particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal,the maximum height attained by it equals $4R$. The angle of projection,$\theta$,is then given by

$A$ 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

$A$ cart moves with a constant speed along a horizontal circular path. From the cart,a particle is thrown up vertically with respect to the cart.