Question

An electron moves to the right with a speed of 0.90c rela- tive 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.

Answer 1

The speed of the proton relative to the laboratory frame is 0.981c

Step-by-step explanation:

Given that,

Speed of electron v= 0.90c

Speed of proton u= 0.70c

We need to calculate the speed of the proton relative to the laboratory frame

Using formula of speed

`u'=(u+v)/(1+(uv)/(c^2))`

Where, u = speed of the proton relative to the electron

v = speed of electron relative to the laboratory frame

Put the value into the formula

`u'=(0.70+0.90)/(1+(0.70*0.90* c^2)/(c^2))`

`u'=c(0.70+0.90)/(1+(0.70*0.90))`

`u'=0.981c`

Hence, The speed of the proton relative to the laboratory frame is 0.981c