Question

Four projectiles are projected with velocities indicated in column II. Match the appropriate description in column I. The projectile is projected from level ground.

$\begin{array}{cccc}& \text{Column - I}& & \text{Column - II}\\ \left(A\right)& \text{Initial speed is maximum}& \left(P\right)& 30\hat{i}+40\hat{j}\\ \left(B\right)& \text{Range is maximum}& \left(Q\right)& 40\hat{i}+30\hat{j}\\ \left(C\right)& \text{Time of flight is maximum}& \left(R\right)& 37\hat{i}+35\hat{j}\\ \left(D\right)& \text{Velocity at the top most point is maximum}& \left(S\right)& 32\hat{i}+40\hat{j}\\ & & \left(T\right)& 10\hat{i}+50\hat{j}\\ & & \left(U\right)& 20\hat{i}+30\hat{j}\end{array}$
Which of the following option has the incorrect combination considering column - I and column - II.

• A. $A\to S$; $B\to R$, $C\to U$; $D\to Q$
• B. $A\to S$; $B\to R$, $C\to T$; $D\to Q$
• C. $A\to R$; $B\to S$, $C\to U$; $D\to Q$
• D. $A\to S$; $B\to R$, $C\to U$; $D\to T$

Answer 1

The correct option is B $A\to S$; $B\to R$, $C\to T$; $D\to Q$

$\left(A\right)$ Initial velocity is $|{\overrightarrow{u}}_i|=\sqrt{u_x^2+u_y^2}$
$\therefore$ Initial velocity is maximum for ${\overrightarrow{u}}_i=32\hat{i}+40\hat{j}$
$\therefore$ $\left(S\right)$ correct
$\left(B\right)$ Range, $R=\frac{2u_x{u}_y}{g}\Rightarrow R\propto u_x{u}_y$
$\therefore$ Maximum for $(37\hat{i}+35\hat{j})$
$\therefore$ $\left(R\right)$ correct
$\left(C\right)T=\frac{2u_y}{g}\propto u_y$
$\therefore \left(T\right)$ is correct
$\left(D\right)$ Velocity at the top most point, $u_y=0$ and
So, maximum velocity at top most point is $u_x\Rightarrow \left(Q\right)$ correct.