A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed $u_0$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V _1$. After hitting the ground, ball rebounds at the same angle $\theta$ but with a reduced speed of $u_0 / \alpha$. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8 V _1$, the value of $\alpha$ is. . . . . .

A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\,m/s$ at an angle of $30^o$ with the horizontal. How far from the throwing point will the ball be at the height of $10\, m$ from the ground ?  $\left[ {g = 10\,m/{s^2},\sin \,{{30}^o} = \frac{1}{2},\cos \,{{30}^o} = \frac{{\sqrt 3 }}{2}} \right]$

A particle covers $50\, m$ distance when projected with an initial speed. On the same surface it will cover a distance, when projected with double the initial speed ......... $m$

A particle is projected at angle $\theta$ with horizontal from ground. The slop $(m)$ of the trajectory of the particle varies with time $(t)$ as ...........

A projectile crosses two walls of equal height $H$ symmetrically as shown The angle of projection of the projectile is

A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \;ms ^{-1}$ and $19.6\; ms ^{-1}$. It will strike the plane after covering distance of ........ $m$