A particle is projected from horizontal making an angle of $53^{\circ}$ with initial velocity $100\,m / s$. The time taken by the particle to make angle $45^{\circ}$ from horizontal is $.........\,s$

A stone is projected from a point on the ground so as to hit a bird on the top of a vertical pole of height $h$ and then attain a maximum height $2 h$ above the ground. If at the instant of projection the bird flies away horizontally with a uniform speed and if the stone hits the bird while descending, then the ratio of the speed of the bird to the horizontal speed of the stone is

For a projectile the ratio of maximum height reached to the square of flight time is

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80\,m / s$. Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly $........\frac{m}{s}$

Two projectiles, one fired from surface of earth with velocity $10 \,m/s$ and other fired  from the surface of another planet with initial speed $5\, m/s$ trace identical trajectories.  The value of acceleration due to the gravity on the planet is   ......... $m/s^2$

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