Trajectories are shown in figure for three footballs. Initially vertical and horizontal velocity components are $u_{y}$ and $u_{x}$ respectively. Ignoring air resistance, choose the correct statements from List-II for the value of variable in List-I

$\begin{matrix} List-I & List-II (I) & Time of flight & (P) & greater for A only (II) & \frac{u_{y}}{u_{x}} & (Q) & greater for C only (III) & u_{x} & (R) & Equal for A and B (IV) & u_{x} u_{y} & (S) & Equal for B and C \end{matrix}$

I \to R; I I \to Q; I I I \to P; I V - S

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I \to R; I I \to P; I I I \to Q; I V - S

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I \to P; I I \to R; I I I \to Q; I V - S

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I \to Q; I I \to P; I I I \to S; I V - R

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Solution

The correct option is B $I \to R; I I \to P; I I I \to Q; I V - S$
(I)Time of flight increases as the maximum height increases. For $A$ and $B$ , time of flight is same.

(II)The ratio $\frac{u_{y}}{u_{x}}$ increases as the range decreases.

(III)Time of flight of $C$ is lowest but the range is sameas that of $B$ , thus in less time $C$ covers the same horizontal displacement as that of $B$ , so it's horizontal velocity is maximum.

(IV) $T = \frac{2 u_{y}}{g}$ and $R = u_{x} T = \frac{2 u_{x} u_{y}}{g}$
So, projectile with maximum range has max value of $u_{y} u_{x}$

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Q. Trajectories are shown in figure for three footballs. Initially vertical and horizontal velocity components are

u_{y}

and

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respectively. Ignoring air resistance, choose the correct statements from List-II for the value of variable in List-I

\begin{matrix} List-I & List-II (I) & Time of flight & (P) & greater for A only (II) & \frac{u_{y}}{u_{x}} & (Q) & greater for C only (III) & u_{x} & (R) & Equal for A and B (IV) & u_{x} u_{y} & (S) & Equal for B and C \end{matrix}

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\to u

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\to F

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