Study Tips: How To Solve Problems in Relative Motion?

This Kinematics tip was contributed by Kshitij, a HashLearn tutor from BITS Pilani, Goa Campus.

With this tip, you will learn:

  • The formula to solve Relative Motion problems
  • The problems you should solve to understand this concept
  • How to determine the application of this formula


The formula to solve these problems is
Vac = Vag - Vcg

To find the relative velocity of particle a with respect to particle c, you have to subtract velocity of c with respect to the ground from velocity of a with respect to the ground.

What kind of problems should I solve to understand this concept?

River-Boat problems and Rain-Man problems are very helpful to understand relative motion. An example of the Rain-Man problem would be as follows:

  • Vrm = Vrg - Vmg where Vrg is the velocity of rain with respect to the ground

  • Vmg is the velocity of man with respect to the ground and

  • Vrm is the velocity of man with respect to rain.

Let's say, Vmg = 10i and Vrg = 20i + 10j, then,
=> Vrm = (20i +10j) - 10i
=> Vrm = 10i + 10j

Therefore, we can conclude that the actual inclination of the rain with respect to the ground is 30 degrees, but to the man, it appears at 45 degrees.


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In what cases should I add up the velocities?

In one dimension, if two vehicles are moving in the opposite direction, then the velocity of two vehicles are added up with respect to the passenger in one of the vehicles.

Note: The basic assumption you must make while solving the problems related with classical mechanics (Newtonian Physics) is that the earth is at rest.


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