## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The electron's speed relative to the proton is $~~0.994~c~~$ toward the left.
Let $u'$ be the electron's velocity relative to the lab reference frame. Let $v$ be the lab's velocity relative to the proton. Let $u$ be the electron's velocity relative to the proton. We can find $u$: $u = \frac{u'+v}{1+\frac{u'v}{c^2}}$ $u = \frac{-0.9c-0.9c}{1+\frac{(-0.9c)(-0.9c)}{c^2}}$ $u = \frac{-1.8c}{1+0.81}$ $u = -0.994~c$ The electron's speed relative to the proton is $~~0.994~c~~$ toward the left.