## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

The length of the spaceship as measured by astronauts on the space station is $~~17.65~m$
We can find the energy generated by the fuel: $E = mc^2$ $E = (2000~kg)(3.0\times 10^8~m/s)^2$ $E = 1.8\times 10^{20}~J$ We can set the spaceship's final kinetic energy equal to this energy to find $\gamma$: $K = (\gamma-1) ~mc^2 = 1.8\times 10^{20}~J$ $\gamma-1 = \frac{1.8\times 10^{20}~J}{mc^2}$ $\gamma = \frac{1.8\times 10^{20}~J}{mc^2}+1$ $\gamma = \frac{1.8\times 10^{20}~J}{(15,000~kg)(3.0\times 10^8~m/s)^2}+1$ $\gamma = 0.1333+1$ $\gamma = 1.1333$ Let $L_0 = 20~m$ We can find the length of the spaceship as measured by astronauts on the space station: $L = \frac{L_0}{\gamma}$ $L = \frac{20~m}{1.1333}$ $L = 17.65~m$ The length of the spaceship as measured by astronauts on the space station is $~~17.65~m$