Two projectiles are thrown with the same range $R$. If their maximum heights are $h_1$ and $h_2$ respectively,then what is the value of the range $R$?

The position coordinates of a projectile projected from the ground on a certain planet (with no atmosphere) are given by $y = (4t - 2t^2) \text{ m}$ and $x = (3t) \text{ m}$,where $t$ is in seconds and the point of projection is taken as the origin. The angle of projection of the projectile with the vertical is ......... (in $^{\circ}$)

$A$ particle is projected from the ground with some initial velocity making an angle of $45^{\circ}$ with the horizontal. If it reaches a height of $7.5 \ m$ above the ground, while it travels a horizontal distance of $10 \ m$ from the point of projection, then the initial speed of the particle is (assume, $g=10 \ m/s^2$): (in $m/s$)

$A$ particle of mass $M$ is moving in a horizontal circle of radius $R$ with uniform speed $v$. When the particle moves from one point to a diametrically opposite point,its

$A$ particle moves along a parabolic path $y = 9x^2$ in such a way that the $x$-component of velocity remains constant and has a value of $\frac{1}{3} \; m/s$. The acceleration of the particle is $....... \; m/s^2$.

$A$ point traversed $3/4$th of the circle of radius $R$ in time $t$. The magnitude of the average velocity of the particle in this time interval is