Question

A driver is reversing his van at a speed of $3m/s$, the driver sees in his rear view mirror (plane mirror) the image of a bus parked behind his van . The speed at which the bus appears to approach the driver is

Answer 1

We know that the plane mirror is a flat mirror which reflects the incident light falling on it. Also, the angle of incidence of the incident angle is equal to the angle of reflecting angle in a plane mirror. Using the given and the property of a plane mirror we can solve the question as shown below.

Complete step-by-step solution:
Let us look at the following properties of a plane mirror, when an object is placed at a distance $y$ from the mirror, the reflection of the object looks like it is $y$ distance into the mirror.
Now since the van is moving at a speed of $3m/s$ and let it cover a distance of $x$ initially, then after $1\;s$ it would cover $x+3$ distance.
Let the bus be visible at the rear mirror at $t=0$ when the van was at $x$ distance, after $1\;s$ , the van would have moved $3\;m$ from the bus. Then the image of the bus on the van would appear to be at a distance $x-3$ from the property of plane mirror.
Then the relative speed at which the bus appears to approach the driver is given as $x+3-(x-3)=6$.
Thus the bus appears to approach at a speed of $6m/s$

Note: This is a very simple question. It only involves the understanding of the relative distances between the bus and the van. Also using the property of plane mirrors we can solve the question very easily. Here we are using relative velocity since the speed or the direction along which the van moves from the bus affects the speed at which the bus appears to approach the van. However, the distance $x$ is irrelevant, as it gets cancelled.