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

Answer:

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

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

$u'=\dfrac{u+v}{1+\dfrac{uv}{c^2}}$

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

$u'=\dfrac{0.70+0.90}{1+\dfrac{0.70\times0.90\times c^2}{c^2}}$

$u'=c\dfrac{0.70+0.90}{1+(0.70\times0.90)}$

$u'=0.981c$

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