For the love of god someone help me understand this. I understand that the KE +

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For the love of god someone help me understand this. I understand that the KE + rest mass Energy = total energy. So finding the rest mass of both protons and the new particle is the total rest mass energy. I'm confused on what to do next. What Mass do use for the total Energy in the eq K = gamma X rest mass

***Please assist me in understanding this I can't wrap my head around how to go about this

Exercise 37.21 Part A Two particles in a high-energy accelerator experiment approach each other head-on with a relative speed of 0.810 c. Both particles travel at What is the speed of each particle, as measured in the laboratory? u= 0.511 c the same speed as measured in the laboratory. Submit My Answers Give Up Correct Provide Feedback Continue

Explanation / Answer

Two particles came towards each other with speed one with speed u’ and the other with a speed v with respect to laboratory.

Then their relative speed is given by

u = (u’+ v) / {1 + (u’v/c²)

When u’ and v are equal in magnitude

u = 2u’ / {1 + (u’/c) ²}

In the given problem u = 0.810c

We have to find u’

Let u’ = nc

0.810c = 2 nc / {1 + n²}

0.810 = 2n / {1 + n²}

Solving

n = 0.511 and n= 1.9585

Since n cannot be greater than 1 we take

n = 0.511

u’ = 0.511c

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