Part A

This question is about the rocket flight example from section 3.7 of the notes. Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a constant velocity of 21 m/s relative to the rocket, the initial mass is 1.1 kg and we take the acceleration due to gravity to be 9.81 ms -2 (a) If it is initially at rest, and after 0.1 seconds the vertical velocity is 1.55 m/s, then what is o, the rate at which it burns fuel, in kg/s ? Enter your answer to 2 decimal places. Number (b) How long does it take until the fuel is all used up? Enter in seconds correct to 2 decimal places. Number (c) If we assume that the mass of the shell is negligible, then what height would we expect the rocket to attain when all of the fuel is used up? Enter an answer in metres to decimal places. (Hint: the solution of the DE doesn't apply when m(t) = 0 but you can look at what happens as m(t) -> 0. The limit lim x Inc = 0 may be useful). Enter in metres (to the nearest metre) NumberUselhe substitution 1 = 45111:, 1 a IVE=2 z (3) Calculate 1,316 :2 in terms oft. to) If the substitution replaces d: with ll) at: then what is the function t)? rm = | (c) Henoe write the integral in terms of t fl to) Perform this integral, including constant of integration c. (e) Convert your answer from a function of t to a function of r. if fr gig to simplify the following integral