Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. (a) If the rocket ejects gas at a relative speed of 2000 m/s and you want the rocket’s speed eventually to be 1.00 X 10-3c, where c is the speed of light in vacuum, what fraction of the initial mass of the rocket and fuel is not? fuel? (b) What is this fraction if the final speed is to be 3000 m/s?

Solution 64E Step 1: Assuming 1 × 10 3 * cfor final speed. v = 0 i v f v i v exhaustln(m 0m) 1.0 × 10 3 * 3 × 10 = 2000 ln*m /m) 0 300000 = 2000 ln(m /m) * 0 150 = ln(m /0)