Answer
0.611c
Work Step by Step
Use the Lorentz Transformation formula for relative velocity.
$v_x=(v'_x+u)/(1+(v'_x u)/c^2 )$
Given in the question that relative velocity is equal to 0.890c and that u and v’x are equal (so let v’x also equal u)
$0.890c=2u/(1+(u)(u))$
Rearrange into a linear quadratic in terms of u
0.890c(u2) -2u + 0.890c = 0
use quadratic formula
$(-b±√(b^2-4ac))/2a$
u = 0.611c or u = 1.64c
however we know that no particle can move at a speed greater than c so u must be equal to 0.611c
therefore u = 0.611c
