The position-time $\left(x-t\right)$ graphs for two children $A$ and $B$ returning from their school $O$ to their home $P$ and $Q$ respectively are shown in diagram. Choose correct entries in the brackets below:

(i) $\left(\frac{A}{B}\right)$ lives closer to the school than $\left(\frac{B}{A}\right)$

(ii) $\left(\frac{A}{B}\right)$ starts from the school earlier than $\left(\frac{B}{A}\right)$

(iii) $\left(\frac{A}{B}\right)$ walks faster than $\left(\frac{B}{A}\right)$

(iv) $A$ and $B$ reach home at the (same/different) time

(v) $\left(\frac{A}{B}\right)$ overtakes $\left(\frac{B}{A}\right)$ overtakes $\left(\frac{B}{A}\right)$ on the road (once/twice).

A particle is projected horizontally as shown from the rim of a large hemispherical bowl. The displacement of the particle when it strikes the bowl the first time is $R$. Find the velocity of the particle at that instant and the time taken.

(i) The velocity of the bomber at the time of release of the bomb.

(ii) The maximum height attained by the bomb

(iii) The horizontal distance travelled by the bomb before its strikes the ground

(iv) The velocity (magnitude & direction) of the bomb just when it strikes the ground.

A body falls freely from some altitude $H$.At the moment the first body starts falling another body is thrown from the earth's surface which collides with the first at an altitude $h=\mathrm{H}/2$. The horizontal is $l$. Find the initial velocity and the angle at which it was thrown.