Answer:
a) [tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]
b) [tex]p=2.81*10^{-16} kg*m/s[/tex]
Explanation:
a) When we have two particles traveling in parallel directions, the formula for relative velocity is:
[tex]\vec{v}_{12}=\frac{\vec{v}_{1}-\vec{v}_{2}}{1-\frac{\vec{v}_{1}\vec{v}_{2}}{c^{2}}}[/tex]
Here we have that v(1) = -v(2), the speed of the of the second particle is the negative of the first one.
If we use these equivalence we have:
[tex]\vec{v}_{12}=\frac{2\vec{v}_{1}}{1+\frac{\vec{v}_{1}^{2}}{c^{2}}}[/tex]
[tex]\vec{v}_{12}=\frac{2*2.19*10^{8}}{1+\frac{2.19*10^{16}}{3*10^{16}}}[/tex]
[tex]\vec{v}_{12}=2.86*10^{8} m/s[/tex]
And, [tex]\vec{v}_{21}=-2.86*10^{8} m/s[/tex]
b) The relativistic momentum equation to one particle observed by the other particle, is:
[tex]p=\gamma mv[/tex]
Where gamma is:
[tex]\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/tex]
Then gamma will be:
[tex]\gamma=\frac{1}{\sqrt{1-\frac{(2.86*10^{8})^{2}}{(3*10^{8})^{2}}}}[/tex]
[tex]\gamma=3.31[/tex]
Finally, the value of the momentum will be:
[tex]p=3.31*2.97*10^{-25}*2.86*10^{8}[/tex]
[tex]p=2.81*10^{-16} kg*m/s[/tex]
I hope it helps you!
