The co-ordinates of a particle moving in $x-y$ plane are given by :  $\mathrm{x}=2+4 \mathrm{t}, \mathrm{y}=3 \mathrm{t}+8 \mathrm{t}^2 .$ The motion of the particle is :

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)$$.......$

Two stones are thrown up vertically and simultaneously but with different speeds. Which graph correctly represents the time variation of their relative positions $\Delta x$.Assume that stones do not bounce after hitting ground.

A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?

$Assertion$ : If a body is thrown upwards, the distance covered by it in the last second of upward motion is about $5\, m$ irrespective of its initial speed
$Reason$ : The distance covered in the last second of upward motion is equal to that covered in the first second of downward motion when the particle is dropped.

Two boys are standing at the ends $A$ and $B$ of a ground where $AB = a$. The boy at $B$ starts running in a direction perpendicular to $AB$ with velocity ${v_1}.$ The boy at $A$ starts running simultaneously with velocity $v$ and catches the other boy in a time $t$, where $t$ is