A particle is projected from ground at an angle $\theta$ with horizontal with speed $u$. The ratio of radius of curvature of its trajectory at point of projection to radius of curvature at maximum height is ........

A particle is projected with speed $u$ at angle $\theta$ with horizontal from ground. If it is at same height from ground at time $t_1$ and $t_2$, then its average velocity in time interval $t_1$ to $t_2$ is .........

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

Shots are fired from the top of a tower and from its bottom simultaneously at angles $30^o$ and $60^o$ as shown. If horizontal distance of the point of collision is at a distance $'a'$ from the tower then height of tower $h$ is :

A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then

A ball of mass $160\, g$ is thrown up at an angle of $60^o$ to the horizontal at a speed of $10\, m\,s^{-1}$ . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ $kg\, m^2/s$  $(g\, = 10\, m\,s^{-2})$