Question

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

$\begin{array}{cccc}& \text{List-I}& & \text{List-II}\\ \text{(I)}& \text{Time of flight}& \text{(P)}& \text{greater for A only}\\ \text{(II)}& \frac{u_y}{u_x}& \text{(Q)}& \text{greater for C only}\\ \text{(III)}& u_x& \text{(R)}& \text{Equal for A and B}\\ \text{(IV)}& u_x{u}_y& \text{(S)}& \text{Equal for B and C}\end{array}$

• A. $I\to R;II\to Q;III\to P;IV-S$
• B. $I\to R;II\to P;III\to Q;IV-S$
• C. $I\to P;II\to R;III\to Q;IV-S$
• D. $I\to Q;II\to P;III\to S;IV-R$

Answer 1

The correct option is B $I\to R;II\to P;III\to Q;IV-S$

(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)$T=\frac{2u_y}{g}$ and $R=u_{x}T=\frac{2u_x{u}_y}{g}$
So, projectile with maximum range has max value of $u_y{u}_x$