Two people are on a train that is moving at 10 m/s north. They are walking 1 m/s south relative to the train. Relative to the ground, their motion is 9 m/s north. Why are we able to use these motions to describe the motion relative to the ground? (1 point) Responses If one object is moving much slower than the speed of light, its speed can be added to that of another object. If one object is moving much slower than the speed of light, its speed can be added to that of another object. The motion of everything in the Universe besides light can be described in this way. The motion of everything in the Universe besides light can be described in this way. The people are moving much slower than the speed of light so the ground acts as a frame of reference. The people are moving much slower than the speed of light so the ground acts as a frame of reference. As long as the frame of reference is stationary, all motion can be described in this way.
The statement that explains why we are able to use these motions to describe the motion relative to the ground is that the people are moving much slower than the speed of light, so classical mechanics (specifically Galilean relativity) applies, and we can use the ground as a frame of reference to add velocities.
In classical mechanics, velocities are additive when objects are moving at speeds much slower than the speed of light. This means that the velocity of one object relative to a particular frame of reference can be added to or subtracted from the velocity of another object to determine their relative velocity.
In the case of the two people walking on the train:
1. The train is moving at 10 m/s north relative to the ground, which is our frame of reference.
2. The people are walking at 1 m/s south relative to the train.
To calculate the velocity of the people relative to the ground, we subtract their velocity relative to the train from the velocity of the train itself because they are walking in the opposite direction that the train is moving:
Velocity of the people relative to the ground = Velocity of the train relative to the ground - Velocity of the people relative to the train
This equals:
10 m/s north (train relative to ground) - 1 m/s south (people relative to train) = 10 m/s - 1 m/s = 9 m/s north (people relative to ground).
This computation is valid in this context because both the train and the people are moving at speeds that are very small compared to the speed of light (approximately 3x10^8 m/s), so the relativistic effects are negligible and Galilean transformations (classical mechanics) apply.