Relative Motion

Relative velocity is the velocity of a body (B) with respect to another moving body (A). It shows how fast and in what direction one object appears to be moving from the perspective of another.

1. Overtaking buses
   • If a fast-moving bus overtakes a slower one, a passenger in the slower bus sees the overtaking bus moving slowly.
2. Stationary observer
   • If the observer is in a stationary bus, the overtaking bus appears to move faster.
3. Moving observer
   • If both observer and object are moving, use the formula:

$V_{BA} = V_B - V_A$

Where:

• $V_{BA}$ is the velocity of body B relative to A
• $V_B$ is the velocity of body B
• $V_A$ is the velocity of body A

Case 1: Same direction

$V_{BA} = V_B - V_A$

Case 2: Opposite directions

$V_{BA} = V_B + V_A$

Note: The relative velocity can also be determined graphically using the triangle or parallelogram methods.

A man swims across a river at 20 m/s, and the river current flows at 10 m/s. Find the resultant velocity and the course if the man swims perpendicular to the current.

Solution

Use scale drawing: Let 1 cm = 2 m/s

1. Swimming velocity (perpendicular to current) = 10 cm (20 m/s)
2. River current (horizontal) = 5 cm (10 m/s)

Use the parallelogram method to draw vectors. The diagonal of the parallelogram represents the resultant velocity.

Measured diagonal = 11.25 cm

Convert to real units:

$11.25 \times 2 = 22.5 \, \text{m/s}$

Angle with river current = 65°25′

Answer:

Resultant velocity = 22.5 m/s

Direction = 65°25′ from the riverbank

1. Doppler effect
   • Change in observed frequency of sound or light due to relative motion between source and observer.
2. Friction
   • The force of friction depends on the relative motion between two surfaces.
3. Planets in space
   • Outer planets appear to move backward due to relative motion with respect to stars and Earth’s movement. This is known as retrograde motion.