A particle $A$ is projected vertically upwards. Another identical particle $B$ is projected at an angle of $45^o $ . Both reach the same height. The ratio of the initial kinetic energy of $A$ to that of $B$ is

A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$, where

An aeroplane moving horizontally at a speed of $200\;m/s$ and at a height of $8\;km$ is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released..........$km$

The horizontal range of a projectile is $4\sqrt 3 $ times its maximum height. Its angle of projection will be    ......... $^o$

A cricket fielder can throw the cricket ball with a speed $v_{0} .$ If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, find

$(a)$ the effective angle to the horizontal at which the ball is projected in air as seen by a spectator

$(b)$ what will be time of flight?

$(c)$ what is the distance (horizontal range) from the point of projection at which the ball will land ?

$(d)$ find $\theta$ at which he should throw the ball that would maximise the horizontal range as  found in $(iii)$.

$(e)$ how does $\theta $ for maximum range change if $u > u_0$. $u =u_0$ $u < v_0$ ?

$(f)$ how does $\theta $ in $(v)$ compare with that for $u=0$ $($ i.e., $45^{o})$ ?

Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^o , 30^o , 45^o $  and $60^o $ with the horizontal respectively. The body having shortest range is