Question

two particles in a particle accelerator are moving towards each other. they each have a speed of 250,000 km/s relative to the ground. how fast will they be moving relative to each other? (1 point)
less than 250,000 km/s
250,000 km/s
between 250,000 and 500,000 km/s
500,000 km/s

Explanation:

Step1: Recall the relativistic velocity - addition formula

The formula for the relative velocity \(u\) of two objects moving with velocities \(v_1\) and \(v_2\) in opposite directions (in the same frame of reference) is \(u=\frac{v_1 + v_2}{1+\frac{v_1v_2}{c^{2}}}\), where \(c = 300000\space km/s\), \(v_1=250000\space km/s\), and \(v_2 = 250000\space km/s\).

Step2: Substitute the values into the formula

Substitute \(v_1 = 250000\space km/s\), \(v_2=250000\space km/s\), and \(c = 300000\space km/s\) into the formula:

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Answer:

Between \(250,000\) and \(500,000\space km/s\)