Question

In an experiment, two protons are shot directly toward each other, each moving at half the speed of light relative to the laboratory. What speed does one proton measure for the other proton?

Answer 1

When two protons are shot directly toward each other at half the speed of light, special relativity's velocity addition formula shows that one proton would measure the other's speed as 0.8 times the speed of light, due to relativistic effects.

Step-by-step explanation:

The question is about the relative speed measured by one proton for another when both protons are shot directly toward each other, each moving at half the speed of light relative to a laboratory frame. In the realm of high-speed particles such as protons moving at a significant fraction of the speed of light, special relativity must be used to calculate the relative speed.

To find the relative speed of one proton as observed by the other, we use the relativistic velocity addition formula:

v' = (v + u) / (1 + (vu/c2))

Where:

• v' is the relative speed of the two protons.
• v and u are the speeds of the two protons, both of which are 0.5c.
• c is the speed of light in a vacuum.

Plugging the values in:

v' = (0.5c + 0.5c) / (1 + (0.5c × 0.5c/c2))

v' = 1c / (1 + 0.25)

v' = 1c / 1.25

v' = 0.8c

Therefore, one proton would measure the speed of the other proton as 0.8 times the speed of light, which is less than the speed of light due to the effects of special relativity.