Classical Mechanics - Special Interest Problem

Start with our expression we derived in class for the velocity of a rocket launched vertically in a uniform gravitational field.

v = vo + g / a (m - mo) + u ln (mo / m)

where m = mo - at. The symbol u represents the exhaust velocity of the thrust, g is the local acceleration due to gravity, and a is the mass burn rate. Both u and a are constant.

  1. Show that the acceleration is given by

    a = -g + ua / m

  2. What should the initial mass (mo) of the rocket be if it is to lift off the launch pad immediately? (For large rockets, the initial mass is slightly greater than this since there is a pre-liftoff burn designed to bring all the systems up to full working efficiency and to check for problems.)
  3. What determines the highest acceleration? When does this occur?

Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.