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 $A$ (see figure) 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 $2.464\, d$ (point $C$ ). Then the height $h _{2}$ is (given tan $\left.30^{\circ}=0.5774\right)$$…….$

The position vector of a particle $\vec R$ as a function of time is given by $\overrightarrow {\;R} = 4\sin \left( {2\pi t} \right)\hat i + 4\cos \left( {2\pi t} \right)\hat j$ where $R$ is in meters, $t$ is in seconds and  $\hat i$ and $\hat j$  denote unit vectors along $x-$ and $y-$directions, respectively. Which one of the following statements is wrong for the motion of particle?