Question

A motorcycle travelling on the highway at a speed of 120km/h passes a car travelling at a speed of 90km/h. From the point of view of a passenger on the car, what is the velocity of the motorcycle?
A) $43km/h$
B) $23km/h$
C) $30km/h$
D) $29km/h$

Answer 1

Hint: Recall the concept of relative velocity. It is defined as the velocity of an object B in the rest frame of another object A. It is the vector difference between the velocities of any two bodies. One of the objects appears to be at rest with the other object. For example if we are travelling in a car, bus or train then the trees, buildings or the other vehicles will appear going backwards. But in actuality they don’t go backward. The trees are stationary but we are moving. So trees appear to move at some relative velocity.

Complete step by step answer:
Given that the speed of the motorcycle is ${v_m} = 120km/h$
Speed of the car is ${v_c} = 90km/h$
The velocity of the motorcycle is calculated by using the concept of relative velocity and can be written by using formula:
$ \Rightarrow {v_{mc}} = {v_m} - {v_c}$
Substituting the given values in the above equation and solving,
$\Rightarrow {v_{mc}} = 120 - 90$
$\Rightarrow {v_{mc}} = 30km/h$
From the point of view of passenger on the car, the velocity of the motorcycle is$ = 30km/h$

Hence, Option C is the right answer.

Note: It is to be noted that relative velocity is important in determining the motion of the objects. It can be known by relative velocity whether an object is at rest or it is moving. But it is different from velocity. This is because the velocity of an object is measured with respect to some reference point or mean position. But relative velocity of the object is measured with respect to a frame. The relative velocity of an object can be negative since it is the difference of the velocities of magnitude of two objects.