The equation of a projectile is $y = \sqrt{3}x - \frac{x^2}{2}$. The velocity of projection is:

$A$ boy standing on a moving truck throws a projectile such that he is able to catch it back after the truck has moved $100 \,m$. If the truck is moving horizontally along a straight line with a constant speed $30 \,m/s$, at what speed (relative to the truck) must the projectile be thrown? (Assume $g = 10 \,m/s^2$)

The range of a projectile when launched at angle $\theta$ is same as when launched at angle $2\theta$. What is the value of $\theta$ (in $^{\circ}$)?

When a ball is thrown with a velocity of $50 \ m s^{-1}$ at an angle $30^{\circ}$ with the horizontal,it remains in the air for how many seconds? (Take $g = 10 \ m s^{-2}$)

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

Match the columns:

Column-$I$ $(R/H_{max})$	Column-$II$ (Angle of projection $\theta$)
$A. 1$	$1. 60^o$
$B. 4$	$2. 30^o$
$C. 4\sqrt{3}$	$3. 45^o$
$D. 4/\sqrt{3}$	$4. \tan^{-1}(4) = 76^o$