From the top of a tower of height $40\,m$, a ball is projected upwards with a speed of $20\,m / s$ at an angle of elevation of $30^{\circ}$. The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (take $g=10\,m / s ^2$ )

A projectile is fired from level ground at an angle $\theta $ above the horizontal. The elevation angle $\phi $ of the highest point as seen from the launch point is related to $\theta $ by the relation

The maximum horizontal range of a projectile is $400\, m$. The maximum value of height attained by it will be    ......... $m$

A bullet is fired from a gun at the speed of $280\,ms ^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is $........\,m$ $\left(g=9.8\,ms ^{-2}, \sin 30^{\circ}=0.5\right):-$

A particle is projected from a point $A$ with velocity $u\sqrt 2$ at an angle of $45^o$ with horizontal as shown in fig. It strikes the plane $BC$ at right angles. The velocity of the particle at the time of collision is

A ball thrown by one player reaches the other in $2$ sec. the maximum height attained by the ball above the point of projection will be about ....... $m$