$A$ projectile is thrown with a velocity of $50 \, m/s$ at an angle of $53^o$ with the horizontal. Determine the instants at which the projectile is at the same height.

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y = (8t - 5t^2) \text{ m}$ and $x = 6t \text{ m}$,where $t$ is in seconds. The acceleration due to gravity on this planet is ......... $m/s^2$.

An aeroplane is flying at a constant horizontal velocity of $600\, km/hr$ at an elevation of $6\, km$ towards a point directly above the target on the earth's surface. At an appropriate time,the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling

Two projectiles are projected with the same initial velocities at $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1 : x$. The value of $x$ is:

$A$ stone is projected at an angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for a short time,the radius of the circular path will be ($g=$ acceleration due to gravity).

The maximum height reached by a projectile is $64 \,m$. If the initial velocity is halved, the new maximum height of the projectile is . . . . . . $m$.