In a colliding-beam experiment, protons moving at 0.800 c in opposite directions strike one another. What is the speed of the incoming proton as viewed by the proton about to be hit?
A) 1.60 c
B) 0.00
C) 0.640 c
D) 0.976 c
E) 0.960 c

Question

Quizplus · Accepted Answer

When two objects move towards each other, their relative speed is the sum of their individual speeds. In this case, the speed of each proton is 0.800 c. Therefore, the speed of the incoming proton as viewed by the proton about to be hit is:

v = 0.800 c + 0.800 c
v = 1.600 c

However, according to the principle of relativity, the speed of an object cannot be greater than the speed of light (c). Therefore, we need to use the relativistic velocity addition formula:

v = (v1 + v2) / (1 + v1v2/c^2)

where v1 = v2 = 0.8c (since the protons have the same speed), and c is the speed of light.

v = (0.8c + 0.8c) / (1 + 0.8c x 0.8c/c^2)
v = 1.6c / (1 + 0.64)
v = 1.6c / 1.64
v = 0.976c

Therefore, the speed of the incoming proton as viewed by the proton about to be hit is 0.976 c, which is closest to answer choice D.

In a Colliding-Beam Experiment, Protons Moving at 0