Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

A hill is $500\, m$ high. Supplies are to be sent across the hill, using a canon that can hurl packets at a speed of $125 \,m/s$ over the hill. The canon is located at a distance of $800 \,m$ from the foot of hill and can be moved on the ground at a speed of $2\, ms^{-1}$; so that its distance from the hill can be adjusted. What is the shortest time in which a packet can reach on the ground across the hill ? Take, $g = 10\, ms^{-2}$.

Two objects are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which these are projected is .........

A projectile is thrown with a velocity of $50\,\, ms^{^{-1}}$ at an angle of $53^o$ with the horizontal Determine the instants at which the projectile is at the same height

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

Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $30^{\circ}$ and its maximum height is $h$, then the maximum height of other will be