Answer
The relativistic momentum is $8.0000000029\times 10^8~kg~m/s$
The non-relativistic momentum is $8\times 10^8~kg~m/s$
The percentage difference is $0.000000036\%$
Work Step by Step
We can find the value of $\gamma$:
$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
$\gamma = \frac{1}{\sqrt{1-\frac{(8\times 10^3~m/s)^2}{(3.0\times 10^8~m/s)^2}}}$
$\gamma = 1.00000000036$
We can find the relativistic momentum:
$p_{rel} = \gamma ~m~v$
$p_{rel} = (1.00000000036)(1\times 10^5~kg)(8\times 10^3~m/s)$
$p_{rel} = 8.0000000029\times 10^8~kg~m/s$
The relativistic momentum is $8.0000000029\times 10^8~kg~m/s$
We can find the non-relativistic momentum:
$p = m~v$
$p = (1\times 10^5~kg)(8\times 10^3~m/s)$
$p = 8\times 10^8~kg~m/s$
The non-relativistic momentum is $8\times 10^8~kg~m/s$
We can find the percentage difference:
$\frac{(8.0000000029\times 10^8~kg~m/s)-(8\times 10^8~kg~m/s)}{8\times 10^8~kg~m/s}\times 100\% = 0.000000036\%$
