Question

My cute puppy, Jenny, saw a mirror for the 1st time in its life. Thinking, of course, that it was another dog she was seeing, she started barking and running towards the mirror with a speed of 10 cm/s. Now, I started moving the mirror towards Jenny with a speed of 5 cm/s, just to mess with her. How fast will Jenny see 'the other dog' (her image) running? (The mirror is a plane mirror. Also, assume Jenny to be a point object, she's tiny, and far from the mirror, so not a bad assumption!)

• A. $30\frac{cm}{s}$, away from her.
• B. $30\frac{cm}{s}$, towards her.
• C. $20\frac{cm}{s}$, towards her
• D. $20\frac{cm}{s}$, away from her.

Answer 1

The correct option is B $30\frac{cm}{s}$, towards her.

As given in the question, let's consider Jenny to be a point object, 'O' and the image in the mirror to be 'I'!
Let's first consider that only the mirror is moving.

We know that the speed of the image is two times speed of the mirror and in the same direction as that of the mirror.
Now,
$\overrightarrow{v_o}=10\frac{cm}{s}\left(right\right)So,\overrightarrow{v_i}=10\frac{cm}{s}\left(left\right)$
Now, to get the net velocity of the image we need to add the velocities obtained in two cases.
Hence,
$\overrightarrow{v_i}=10\frac{cm}{s}\left(left\right)+10\frac{cm}{s}\left(left\right)$
$=20\frac{cm}{s}\left(left\right)$

Therefore, Jenny will see her image to be running with velocity, $\overrightarrow{v_{i,o}}=\overrightarrow{v_i}-\overrightarrow{v_i}=20\frac{cm}{s}\left(left\right)-10\frac{cm}{s}\left(right\right)=30\frac{cm}{s}\left(left\right),or30\frac{cm}{s}$towards her.