A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

A projectile is fired at a speed of $100\, m/sec$ at an angle of $37^o$ above the horizontal. At the highest point, the projectile breaks into two parts of mass ratio $1:3$, the smaller coming to rest. Then the distance of heavier part from the launching point is ........... $m$.

Two objects are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is .........

A fighter plane is flying horizontally at a height of $250\  m$ from ground with constant velocity of $500\  m/s$. It passes exactly over a cannon which can fire a shell at any time in any direction with a speed of  $100\  m/s$. Find the duration of time  for which the plane is in danger of being hit by a cannon shell

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 $4 \mathrm{R}$. The angle of projection, $\theta$, is then given by

A ball is thrown from the ground to clear a wall $3\,m$ high at a distance of $6\,m$ and falls $18\,m$ away from the wall, the angle of projection of ball is