We want to find the frame of reference (viewpoint) where the cup of coffee inside your car moves the fastest.
The correct option will be A, the astronaut in the ISS.
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Let's see how to get the correct option, first, remember that the frame of reference means the "viewpoint" that you are taking. So we need to find the viewpoint where the cup of coffee moves faster.
Now just let's analyze all the given options to see in which one the cup moves fastest.
A) Here the astronaut sees the car moving, so here the cup has the speed of the car, and the astronaut is also moving. Remember that the International Space Station orbits with a speed of 7.6km/s (this is really fast). So in the frame of reference of the astronaut, he/she is at a stop, so this velocity is assigned to all the other objects. Thus, he sees the cup of coffee moving really fast.
B) In it's own frame of reference, the cup does not move.
C) The observer will see the car moving, and the cup is inside the car, so in this frame of reference the velocity of the cup is the same as the one of the car.
D) The incoming car has a given velocity V', from this frame, the car with the cup of coffee will have its own velocity plus the V' of the incoming car, so from this frame the velocity of the cup of coffee is larger than the velocity of the car with the cup.
E) You are driving the car with the cup of coffee, so the cup of coffee is always next to you, so in this frame, the cup does not move.
Concluding, is easy to see that the frame of reference where the cup moves the fastest is in the first one, for the nature of the astronaut's frame of reference velocity, he/she will see the cup moving the fastest.
If you want to learn more, you can read:
https://brainly.com/question/12222532
