A projectile is launched at an angle ' $\alpha$ ' with the horizontal with a velocity $20 \; ms ^{-1}$. After $10 s$, its inclination with horizontal is ' $\beta$ '. The value of $\tan \beta$ will be : $\left( g =10 \; ms ^{-2}\right)$

The range of a particle when launched at an angle of ${15^o}$ with the horizontal is $1.5 \,km$. What is the range of the projectile when launched at an angle of ${45^o}$ to the horizontal ........ $km$

Two bodies are thrown up at angles of $45^o $ and $60^o $, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

For a projectile, the ratio of maximum height reached to the square of flight time is ($g = 10 ms^{-2}$)

What is range of the projectile particle ? Give velocity of projectile particle at maximum height.

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   ......... $m/s^2$