The fastest vehicle flown by humans on a regular basis is the Space Shuttle which has a mass of about \(1 \times 10^{5} \mathrm{kg}\) and travels at a speed of about \(8 \times 10^{3} \mathrm{m} / \mathrm{s} .\) Find the momentum of the Space Shuttle using relativistic formulae and then again by using nonrelativistic formulae. By what percent do the relativistic and nonrelativistic momenta of the Space Shuttle differ? [Hint: You might want to use one of the approximations in Appendix A.5.]

Question: Calculate the relativistic and nonrelativistic momenta of a Space Shuttle with mass \(1 \times 10^5 kg\) and speed \(8 \times 10^3 m/s\), and find the percentage difference between the two momenta. To calculate the relativistic and nonrelativistic momenta of the Space Shuttle, follow the three steps: 1. Find the relativistic momentum using the formula \(p = \dfrac{mv}{\sqrt{1 - \dfrac{v^2}{c^2}}}\), where m is the mass, v is the speed, and c is the speed of light. 2. Find the nonrelativistic momentum using the formula \(p = mv\), where m is the mass and v is the speed. 3. Compute the percentage difference between the momenta using the formula \(\dfrac{|p_{rel} - p_{nr}|}{p_{nr}} \times 100\%\). Upon following this procedure, you will obtain the relativistic momentum \(p_{rel}\), the nonrelativistic momentum \(p_{nr}\), and the percentage difference between the two momenta.