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)$$.......$

A particle has initial velocity of $\left( {\widehat i + \widehat j} \right)\, m/s$ and an acceleration of $\left( {\widehat i + \widehat j} \right)\, m/s^2$. Its speed after $10s$ will be :-

The position of a projectile launched from the origin at $t=0$ is given by $\vec{r}=(40 \hat{i}+50 \hat{j}) m$ at $t=$ $2 s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g =10\,ms ^{-2}$ )

A car travels $6\, km$ towards north at an angle of $45^o$ to the east and then travels distance of $4\, km$ towards north at an angle $135^o$ to east. How far is the point from the starting point? What angle does the straight line joining its initial and final position makes with the east?

The position of a particle moving in the $xy-$plane at any time $t$ is given by $x = (3{t^2} - 6t)$ metres, $y = ({t^2} - 2t)$ metres. Select the correct statement about the moving particle from the following

The equation of a projectile is $y=a x-b x^2$. Its horizontal range is ......