A particle is projected with some angle from the surface of the planet. The motion of the particle i

Question

A particle is projected with some angle from the surface of the planet. The motion of the particle is described by the equation; $x=t, y=t-t^2$. Column I contains parameters and column II contains magnitudes only. Then match the following columns :

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4. (c) : (A) ? (Q); (B) ? (R); (C) ? (P); (D) ? (S)
$(\mathrm{A}) ightarrow(\mathrm{Q}): u_x=\frac{d x}{d t}=1$ and $u_y=\frac{d x}{d t}=1-2 t$
$	herefore \quad u_{t=0}=\sqrt{u_x^2+u_y^2}=\sqrt{1^2+1^2}=\sqrt{2} \mathrm{~m} \mathrm{~s}^{-1}$.
$(\mathrm{B}) ightarrow(\mathrm{R}): a_x=\frac{d^2 x}{d t^2}=0$ and $a_y=\frac{d^2 y}{d t^2}=-2$
$(\mathrm{C}) ightarrow(\mathrm{P}):$ For time of flight, $y=0$ or $\quad 0=t-t^2$
$
	herefore \quad t=1 \mathrm{~s} .
$
$(\mathrm{D}) ightarrow(\mathrm{S}):$ For maximum height, $t=\frac{1}{2} \mathrm{~s}$.
$	herefore \quad H=t-t^2=\frac{1}{2}-\left(\frac{1}{2}ight)^2=\frac{1}{4} \mathrm{~m}$.