Two stones having different masses $m_1$ and $m_2$ are projected at an angle $\alpha$ and $\left(90^{\circ}-\alpha\right)$ with same speed from same point. The ratio of their maximum heights is

A projectile is thrown with some initial velocity at an angle $\alpha$ to the horizontal. Its velocity when it is at the highest point is $(2 / 5)^{1 / 2}$ times the velocity when it is at height half of the maximum height. Find the angle of projection $\alpha$ with the horizontal.

If $R$ and $H$ are the horizontal range and maximum height attained by a projectile, than its speed of projection is ..........

A body of mass $1\,kg$ is projected with velocity $50\,m / s$ at an angle of $30^{\circ}$ with the horizontal. At the highest point of its path a force $10\,N$ starts acting on body for $5\,s$ vertically upward besides gravitational force, what is horizontal range of the body? $\left(g=10\,m/s^2\right)$

A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is

A projectile is projected with kinetic energy $K$. If it has the maximum possible horizontal range, then its kinetic energy at the highest point will be ......... $K$