# Basic special relativity addition of velocities problem

"An electron moves to the right with a speed of 0.90c relative
to the laboratory frame. A proton moves to the right
with a speed of 0.70c relative to the electron. Find the
speed of the proton relative to the laboratory frame."

u' = (u-v)/(1-(uv/c2)) where u will be velocity of electron with respect to lab frame, v is velocity of proton with respect to lab frame and u' is their relative velocity. ie, u=0.9c, u'=0.7c

Solving for v yields 0.54c. But my solutions book says 0.98c? Im pretty sure they are wrong...it would be 0.98c if the proton were moving to the left with respect to electron...am i right?

## The Attempt at a Solution

Related Introductory Physics Homework Help News on Phys.org
Janus
Staff Emeritus
Gold Member
u' = (u-v)/(1-(uv/c2)) where u will be velocity of electron with respect to lab frame, Correct.
v is velocity of proton with respect to lab frame
No, v is the velocity of the proton with respect to the electron
and u' is their relative velocity.
No, u' is the velocity of the proton with respect to the lab, which is what you were asked to find.

The proton is moving faster than the electron and in the lab frame the electron is seen as moving 0.90c so you know that the proton is moving faster than that in the lab frame.

I think you need to reevaluate your formula or what you are defining the variables as.

No, v is the velocity of the proton with respect to the electron

No, u' is the velocity of the proton with respect to the lab, which is what you were asked to find.
According to my book this formula was derived u' being the relative velocity and v being the velocity with respect to lab..

nvm i got it!
v would be the electron speed rel to lab and u' the proton speed rel to electron