Two bodies are projected at angles $\theta$ and $(90^\circ - \theta)$ with the same initial velocity. Find the ratio of their times of flight.

Average velocity of a particle in projectile motion between its starting point and the highest point of its trajectory is: (projection speed = $u$,angle of projection from horizontal = $\theta$)

$A$ football player throws a ball with a velocity of $50 \ m/s$ at an angle of $30^{\circ}$ from the horizontal. The ball remains in the air for ...... $s$ $(g = 10 \ m/s^2)$.

In the climax of a movie,the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After some time,when they are at the same horizontal level,the villain fires a bullet horizontally towards the hero. Both the hero and the villain are falling with a constant downward acceleration of $2\ m/s^2$ due to their parachutes. Assuming the hero is within the range of the bullet and air resistance on the bullet is negligible,which of the following is correct?

Galileo,in his book $Two \text{ } new \text{ } sciences$,stated that "for elevations which exceed or fall short of $45^{\circ}$ by equal amounts,the ranges are equal". Prove this statement.

$A$ $1.5 \,kg$ ball is shot upward at an angle of $34^{\circ}$ to the horizontal with an initial speed of $20 \,m/s$. The maximum height reached by the ball is (use $\cos 34^{\circ} = 0.83$ and $\sin 34^{\circ} = 0.56$): (in $\,m$)