The equation of motion of a projectile is $y=12 x-\frac{3}{4} x^2$ $..........\,m$ is the range of the projectile.

A stone projected with a velocity u at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity u at an angle $\left( {\frac{\pi }{2} - \theta } \right)$ with the horizontal, it reaches maximum height $ H_2$. The relation between the horizontal range R of the projectile, $H_1$ and $H_2$ is

Define projectile particle and derive the equation $y\, = \,(\tan \,{\theta _0})x\, - \,\frac{g}{{(2\,\cos \,{\theta _0})}}{x^2}$

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 ball of mass $m$ is thrown vertically upwards. Another ball of mass $2m$ is thrown at an angle $\theta $ with the vertical. Both of them stay in air for same period of time. The heights attained by the two balls are in the ratio of

A ball is projected from a point $O$ as shown in figure. It will strike the ground after ........ $s$ $\left(g=10 \,m / s ^2\right)$