Chapter 14.3, Problem 14.93P

A rocket sled bums fuel at the constant rate of 120 lb/s. The initial weight of the sled is 1800 lb. including 360 lb of fuel. Assume that the track is lubricated and the sled is aerodynamically designed so that air resistance and friction are negligible. (a) Derive a formula for the acceleration a of the sled as a function of time t and the exhaust velocity $v_{ex}$ of the burned fuel relative to the sled. Plot the ratio $a/v_{ex}$ versus time r for the range 0 < t < 4 s. and check the slope of the graph at t = 0 and t = 4 s using the formula for a. (b) Determine the ratio of the velocity v_b of the sled at burnout to the exhaust velocity $v_{ex}$