Question

A meteorite of mass 1500 kg moves with a speed of 0.700 c . Find the magnitude of its momentum p.

Answer 1

`4.4\cdot 10^(11) kg m/s`

Step-by-step explanation:

Since the meteorite is moving at a speed which is a significant fraction of the speed of light, we must use the formula for the relativistic momentum:

`p=\gamma m_0 v`

where

`\gamma = \frac{1}{\sqrt{1-(v^2)/(c^2)}}` is the relativistic factor

`m_0 = 1500 kg` is the rest mass of the meteorite

`v=0.700 c` is the speed of the meteorite

First of all, let's find the relativistic factor

`\gamma = \frac{1}{\sqrt{1-((0.700 c)^2)/(c^2)}}=1.4`

And since
`c=3.0\cdot 10^8 m/s`, the speed of the meteorite is

`v=(0.700)(3\cdot 10^8 m/s)=2.1\cdot 10^8 m/s`

So now we can find the momentum of the meteorite

`p=\gamma m_0 v=(1.4)(1500 kg)(2.1\cdot 10^8 m/s)=4.4\cdot 10^(11) kg m/s`