Relative velocity
When you are traveling in a car or bus or train, you see the trees, buildings and many other things outside going
backwards. But are they really going backwards? No, you know it pretty well that it’s your vehicle that is
moving while the trees are stationary on the ground. But then why do the trees appear to be moving backwards?
Also the co-passengers with you who are moving appear stationary to you despite moving.
It’s because in your frame both you and your co-passengers are moving together. Which means there is no
relative velocity between you and the passengers. Whereas the trees are stationary while you are moving.
Therefore trees are moving at some relative velocity with respect to you and the other passenger. And that
relative velocity is the difference of velocities between you and the tree.
The rule of thumb is to consider one body at rest and evaluate how much the displacement is changing per second.
That’s our relative velocity. Let’s consider the scenarios below –
Here the two cars are moving away from
each other. Therefore every second the
displacement between them changes
(increases) by 10m. Therefore the
velocity of A relative to B is 10ms-1
Here the two cars are moving towards each
other. Therefore every second the displace-
ment between them changes (decreases)
by 10m. Therefore the velocity of A relative
to B is 10ms-1
In this scenario, the two cars are moving in
the same direction with the same speed
there is no change in displacement between
the cars. Therefore the velocity of A relative
to B would be zero.
From the scenarios, we can conclude that when two bodies are moving in opposite directions, their speeds are added
to find the relative speed
Similarly, when two bodies are moving in the same direction, their speeds are subtracted to find the relative velocity
Mathematical examples from Question Paper
Example 1: January 2015 WPH01 Question 14
A man is walking at a constant horizontal velocity of 1.2 ms-1 in the rain.
To the man the rain appears to be falling vertically at a velocity of 1.8 ms-1.
Draw a labelled vector diagram, to scale, and use it to determine the actual velocity of the rain. (5)
Example 2: Jan 2017 WPH01 Question 15 (d)
The skydiver’s jump was being filmed by another skydiver. Both skydivers jumped out of the plane
at the same time. During the period of filming only the skydiver who was being recorded opened his
parachute. When viewing the recording after the jump, it appeared as though the skydiver being
filmed moved upwards as he opened his parachute. Explain this apparent movement.
(2)
