3.11⋆⋆ (a) Consider a rocket traveling in a straight line subject to an external force Fext acting along the same line. Show that the equation of motion is mv = -mvex + Fext (3.29) [Review the derivation of Equation (3.6) but keep the external force term.] (b) Specialize to the case of a rocket taking off vertically (from rest) in a gravitational field g, so the equation of motion becomes mv = -mvex-mg. (3.30) Assume that the rocket ejects mass at a constant rate, m = −k (where k is a positive constant), so that m = mo kt. Solve equation (3.30) for v as a function of t, using separation of variables (that is, rewriting the equation so that all terms involving u are on the left and all terms involving t on the right). (c) Using the rough data from Problem 3.7, find the space shuttle's speed two minutes into flight, assuming (what is nearly true) that it travels vertically up during this period and that g doesn't change appreciably. Compare with the corresponding result if there were no gravity. (d) Describe what would - Problems for Chapter 3 101 happen to a rocket that was designed so that the first term on the right of Equation (3.30) was smaller than the initial value of the second.

3.11⋆⋆ (a) Consider a rocket traveling in a straight line subject to an external force Fext acting along the same line. Show that the equation of motion is mv = -mvex + Fext (3.29) [Review the derivation of Equation (3.6) but keep the external force term.] (b) Specialize to the case of a rocket taking off vertically (from rest) in a gravitational field g, so the equation of motion becomes mv = -mvex-mg. (3.30) Assume that the rocket ejects mass at a constant rate, m = −k (where k is a positive constant), so that m = mo kt. Solve equation (3.30) for v as a function of t, using separation of variables (that is, rewriting the equation so that all terms involving u are on the left and all terms involving t on the right). (c) Using the rough data from Problem 3.7, find the space shuttle's speed two minutes into flight, assuming (what is nearly true) that it travels vertically up during this period and that g doesn't change appreciably. Compare with the corresponding result if there were no gravity. (d) Describe what would - Problems for Chapter 3 101 happen to a rocket that was designed so that the first term on the right of Equation (3.30) was smaller than the initial value of the second.