Question

A ball at rest is projected horizontally from a table in front of a vertical plane mirror as shown in the figure. At any time $t$, the velocity of image with respect to ground can be written as :

• A. $-u\hat{i}$
• B. $u\hat{i}+gt\hat{j}$
• C. $-u\hat{i}-gt\hat{j}$
• D. $u\hat{i}-gt\hat{j}$

Answer 1

The correct option is C $-u\hat{i}-gt\hat{j}$

The velocity of the object at any time $t$,
$\overrightarrow{v_o}=u_x\hat{i}+u_y\hat{j}$
$\Rightarrow \overrightarrow{v_o}=u\hat{i}+(0-gt)\hat{j}$
$[v=u+at]$
$\Rightarrow \overrightarrow{v_o}=u\hat{i}-gt\hat{j}$
We know that for fixed plane mirror,
$\left(1\right)$ Perpendicular to the mirror ($x$ - axis), $v_o=-v_i$
$\left(2\right)$ Parallel to the mirror ($y$ - axis), $v_o=v_i$
So,
The velocity of the image at any time $t$,
$\overrightarrow{v_i}=-u_x\hat{i}+u_y\hat{j}$
$\Rightarrow \overrightarrow{v_i}=-u\hat{i}-gt\hat{j}$