Relative Motion

Step 1: Understanding the Problem 1. When the escalator is stationary, Ruma walks with a velocity and takes time to reach the top. The height of the escalator can be related to the time and velocity: 2. When the escalator is moving with velocity , and Ruma is stationary on the escalator, the time taken to reach the top is . The total velocity of Ruma on the moving escalator is and the distance is covered in time : Step 2: Time to Walk Up the Moving Escalator If Ruma is walking with velocity on the moving escalator, her effective velocity will be (since both velocities add up when moving in the same direction). The time taken to cover the distance will be: Step 3: Substituting Values for From the equations above for , we substitute from both the cases (stationary escalator and moving escalator) into the equation for : Step 4: Conclusion The time taken by Ruma to walk up with velocity on the moving escalator is given by: Now, comparing this equation with the given options, we find that the correct choice is Option (C). Final Answer: The correct answer is:

Concept: Let escalator length = . Step 1: {\color{red}Stationary escalator.} Step 2: {\color{red}Standing on moving escalator.} Step 3: {\color{red}Both moving.} Net speed: Time: Step 4: {\color{red}Substitute.}