In which of these situations is it reasonable to use the approximate equation for the momentum of an object, instead of the full relativistically correct equation? (1) A car traveling on an interstate highway (2) A commercial jet airliner flying between New York and Seattle (3) A neutron traveling at 2700 meters per second (4) A proton in outer space traveling at $\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{8}}$ m/s (5) An electron in a television tube traveling$\mathbf{3}\mathbf{\times }{\mathbf{10}}^{\mathbf{6}}$ m/s.

1. The velocity of the car is very less compared to the speed of light. So, the value of$\mathrm{\gamma }$ is very close to one in this case. Therefore, approximate equation for the momentum can be used here.

2. The Airliner’s velocity is not even close to the speed of light. So, the value of$\gamma$ is very close to one in this case. Therefore, approximate equation for the momentum can be used here.

3. The velocity of neutron is 2700 meters per second. It is still very less than the speed of light. So, the value of$\gamma$ is very close to one in this case. Therefore, approximate equation for the momentum can be used here.

4 The velocity of proton is close to that of light. So, in this case $\gamma$will have a significant value. Therefore, full relativistically correct equation must be used here.

5. The velocity of electron is very high. But is still less than the velocity of light. So, the value of $\gamma$is very close to one in this case. Therefore, approximate equation for the momentum can be used here.