The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is:

Four objects $P, Q, R,$ and $S$ are projected with the same velocity at angles of $15^o, 30^o, 45^o,$ and $60^o$ respectively. Which of these will have the minimum range?

$A$ bullet fired from a gun falls at a distance half of its maximum range. The angle of projection of the bullet is (in $^{\circ}$)

If a body projected with a velocity of $19.6 \ m/s$ reaches a maximum height of $9.8 \ m$, then the range of the projectile is (Neglect air resistance). (in $m$)

The equation of motion of a projectile is $y = Ax - Bx^2$ where $A$ and $B$ are constants of motion. The horizontal range of the projectile is

$A$ boy throws a ball into the air at $45^{\circ}$ from the horizontal to land it on the roof of a building of height $H$. If the ball attains maximum height in $2 \text{ s}$ and lands on the building in $3 \text{ s}$ after launch, then the value of $H$ is . . . . . . $\text{m}$. $(g = 10 \text{ m/s}^2)$