Final answer:
Relative velocity in physics involves using vector addition to calculate the speed of one object in relation to another. In the case of a man running perpendicular to a train track while a train moves along the track, trigonometry or the Pythagorean theorem may be needed to find the resultant relative speed.
Step-by-step explanation:
The student's question pertains to the concept of relative velocity in physics. When considering the scenario where a man is running perpendicular to the train track away from the track, and a train moving parallel to the track at different speeds, the speed of the man with respect to a passenger in the train can be calculated using vector addition of velocities.
If the man runs at a speed of 12 m/s and the train moves at 30 m/s, you need to consider the direction of movement for both and perform vector addition. The specifics would vary based on the angle between the path of the man and the train, which isn't provided in this question. Generally, this would require applying the Pythagorean theorem or trigonometric functions to find the resultant relative speed if the directions are not collinear.