Verified 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

u = (u’+ v) / {1 + (u’v/c²)

When u’ and v are equal in magnitude

u = 2u’ / {1 + (u’/c) ²}

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In the given problem u = 0.89c

Let u’ = nc

0.89c = 2 nc / {1 + n ²}

0.89 = 2 n / {1 + n ²}

Solving

n = 0.611 and

n= 1.635

Since n cannot be greater than 1 we take

n =0.611

u’ = 0.611c

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