$A$ shell fired from the base of a mountain just clears it. If $\alpha$ is the angle of projection,then the angular elevation of the summit $\beta$ is

The relation between the horizontal displacement $x$ (in metre) and the vertical displacement $y$ (in metre) of a projectile is $y = 3x - 0.8x^2$. The time of flight of the projectile is (Acceleration due to gravity $g = 10 \ m/s^2$). (in $s$)

$A$ football player throws a ball with a velocity of $50 \ m/s$ at an angle of $30^{\circ}$ from the horizontal. The ball remains in the air for ...... $s$ $(g = 10 \ m/s^2)$.

The range of a particle when launched at an angle of $15^\circ$ with the horizontal is $1.5 \, km$. What is the range of the projectile when launched at an angle of $45^\circ$ to the horizontal? (in $km$)

$A$ bullet is fired with a speed of $1000 \, m/s$ in order to hit a target $100 \, m$ away. If $g = 10 \, m/s^2$,the gun should be aimed:

Two towers $A$ and $B$,each of height $20 \ m$,are situated a distance $200 \ m$ apart. $A$ body thrown horizontally from the top of the tower $A$ with a velocity $20 \ ms^{-1}$ towards the tower $B$ hits the ground at point $P$,and another body thrown horizontally from the top of tower $B$ with a velocity $30 \ ms^{-1}$ towards the tower $A$ hits the ground at point $Q$. If a car starting from rest from $P$ reaches $Q$ in $10 \ s$,then the acceleration of the car is (acceleration due to gravity $g = 10 \ ms^{-2}$): (in $ms^{-2}$)