At any instant $t$, the vertical distance $Y$ and horizontal distance $X$ of a projectile are given by $2Y = 6t - gt^2$ and $X = 4t$. The initial velocity of the projectile is ($X$ and $Y$ are in $m$ and $t$ is in $s$). (in $\,m/s$)

$A$ projectile is thrown at an angle of $\pi/3$ with the horizontal,reaching a maximum height $Y$. If another projectile is thrown with the same initial velocity at an angle of $\pi/6$,what will be the maximum height attained?

The equation of a projectile is $y = 16x - \frac{5x^2}{4}$. The horizontal range is .......... $m$.

$A$ helicopter is flying horizontally with a speed $v$ at an altitude $h$ and has to drop a food packet for a man on the ground. What is the distance of the helicopter from the man when the food packet is dropped?

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

$A$ particle of mass $m$ is projected with a velocity $u$ making an angle of $30^{\circ}$ with the horizontal. The magnitude of the angular momentum of the projectile about the point of projection when the particle is at its maximum height $h$ is: