Two objects are projected with the same velocity '$u$' but at different angles $\alpha$ and $\beta$ with the horizontal. If $\alpha + \beta = 90^{\circ}$,the ratio of the horizontal range of the first object to the $2^{\text{nd}}$ object will be:

$A$ boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give an explanation to support your diagram.

$A$ particle is projected at $60^\circ$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is

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

If the kinetic energy of a second ball at its maximum height is $K$,what will be the kinetic energy of the first ball at its maximum height? (Assuming the first ball is thrown vertically upwards).

The initial velocity of a projectile is given by $v = a\hat{i} + b\hat{j}$. If the range $R$ is twice the maximum height $H$,then which of the following is true?