$A$ boy walks uniformly along the sides of a rectangular park of size $400 \, m \times 300 \, m$,starting from one corner to the diagonally opposite corner. Which of the following statements is incorrect?

$A$ 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 $\tan 30^{\circ} = 0.5774$):

What is motion?

The position vector of a particle is given by the expression $\vec{r} = 3t^2 \hat{i} + 4t^2 \hat{j} + 7 \hat{k}$. The distance traversed in the first $10 \, s$ is ......... $m$.

What is mechanics? Give definitions of its sub-branches.

On an open ground,a motorist follows a track that turns to his left by an angle of $60^{\circ}$ after every $500\; m$. Starting from a given turn,specify the displacement of the motorist at the third,sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.