JEE Main 2020, 2 Sep Shift-I
LEVELJEE Main
Visualized Solution
The Sigma Insight: Relative Velocity
Have you ever sat in a train, looked out the window at another train passing by, and felt like you were moving incredibly fast? That dizzying sensation is the magic of relative velocity.
In this problem, we are going to untangle a beautiful scenario involving two trains moving in opposite directions, and a passenger who decides to take a stroll inside one of them. Let's break it down step by step.
Setting the Scene
We have Train and Train running on parallel tracks. Train is moving at , and Train is moving in the opposite direction at .
Inside Train , a person is walking opposite to the train's motion at . Our goal is to find out how fast this person appears to be moving from the perspective of someone sitting in Train .
To avoid any confusion, we must establish a strict sign convention. Let's define the direction of Train as the positive -direction.
This means:
The Ground Reality
Before we can figure out what Train sees, we need to know what a stationary observer on the ground sees.
The person is walking on a moving platform (Train ). Therefore, their actual velocity with respect to the ground () is the vector sum of the train's velocity and their walking velocity.
Substituting our values:
Even though the person is walking backwards, the train is carrying them forward much faster. So, to someone standing on the ground, the person is moving forward at .
Shifting the Frame of Reference
Now comes the fun part. We need to shift our perspective to Train .
The relative velocity of the person with respect to Train () is calculated by subtracting Train 's velocity from the person's ground velocity.
Let's plug in the numbers:
Notice how the minus signs cancel out? Because they are moving in opposite directions, their speeds effectively add up, creating a much higher relative speed.
The Final Catch
Units
We have our answer, but there is a catch. The question specifically asks for the speed in meters per second (), not kilometers per hour.
We must multiply our result by the conversion factor .
And there we have it! To an observer on Train , the person appears to be zooming past at exactly .
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