What is kinematics?

How can we determine whether an object is at rest or not?

Explain with an example that the magnitude of displacement may be zero but the corresponding path length is not zero.

Under what condition is the magnitude of distance covered by an object equal to its displacement?

Distinguish between path length and displacement.

$A$ balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_{1}$,a girl standing at a distance $d$ (point $B$) from $A$ sees it at an angle $45^{\circ}$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$,it is seen at an angle $60^{\circ}$ with respect to the vertical if the girl moves further by a distance $2.464d$ (point $C$). Then the height $h_{2}$ is (given $\tan 30^{\circ} = 0.5774$):