Question

A ball is projected from top of a table with initial velocity $u$ at an angle $\theta$ with the horizontal as shown in the figure. The motion of image of ball with respect to the ball will be
$($Consider the plane mirror of sufficient height$)$

• A. a projectile
• B. straight line along vertical direction
• C. straight line along horizontal direction
• D. straight line or projectile depends on angle $\theta$

Answer 1

The correct option is C straight line along horizontal direction

The velocity and acceleration of the image and object have been shown below in the figure.


Relative acceleration between image and object, ${\overrightarrow{a}}_{IO}=0$
Velocity of image $w.r.t$ object,
${\overrightarrow{v}}_{IO}={\overrightarrow{v}}_I-{\overrightarrow{v}}_O$
$\Rightarrow {\overrightarrow{v}}_{IO}=-u\cos \theta \hat{i}+u\sin \theta \hat{j}-(u\cos \theta \hat{i}+u\sin \theta \hat{j})$
$\Rightarrow {\overrightarrow{v}}_{IO}=-2u\cos \theta \hat{i}$
Thus, ${\overrightarrow{v}}_{IO}$ is along negative $x$ -direction.
Hence, the path of motion is a straight line along $x$ axis or horizontal.