Match list I with list II for a projectile.
List - I List - II
A. For two angles $θ$ and $(90^{\circ} - θ)$ with same magnitude of velocity of projection e. $\frac{P \bar{i} . P \bar{i}}{g}$
B. Equation of parabola of a projectile, $y = Px - {Qx}^{2}$ f. Maximum height = 25% of $\frac{P^{2}}{Q}$
C. Radius of curvature of path of projectile projected with a velocity $(P \bar{i} + Q \bar{j}) {ms}^{- 1}$ at highest point g. Range = Maximum height
D. Angle of projection $θ$ = Tan^-1(4) h. Range is same
A B C D
1. f h g e
2. h f e g
3. e g f h
4. e g h f

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answer is B.

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Detailed Solution

For complementary angle of projection, ranges are same.

For Equation of parabola of a projectile, $y = Px - {Qx}^{2}$ :

$H = \frac{P^{2}}{4 Q} = 25 % of \frac{P^{2}}{Q}$

Radius of curvature of path of projectile projected with a velocity $(P \bar{i} + Q \bar{j}) {ms}^{- 1}$ at highest point :

$R = \frac{{v_{x}}^{2}}{g} = \frac{P^{2}}{g} = \frac{P \bar{i} \cdot P \bar{i}}{g}$

again, $θ = \tan^{- 1} (\frac{4 H}{R}) = \tan^{- 1} (4)$

$\Rightarrow R = H$

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	List - I		List - II
A.	For two angles $θ$ and $(90^{\circ} - θ)$ with same magnitude of velocity of projection	e.	$\frac{P \bar{i} . P \bar{i}}{g}$
B.	Equation of parabola of a projectile, $y = Px - {Qx}^{2}$	f.	Maximum height = 25% of $\frac{P^{2}}{Q}$
C.	Radius of curvature of path of projectile projected with a velocity $(P \bar{i} + Q \bar{j}) {ms}^{- 1}$ at highest point	g.	Range = Maximum height
D.	Angle of projection $θ$ = Tan^-1(4)	h.	Range is same