Motion in Straight Line question bank (Physics)

The position of a particle along the $x$-axis at time $t$ is given by $x = 2 + t - 3t^2$. The displacement and the distance travelled in the interval $t = 0$ to $t = 1$ are respectively:

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