# HW6 - A m the area-to-mass ratio and v V r the relative...

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MAE146: Astronautics – Homework Assigned: Wednesday, January 27 th , 2010 Due date: Friday , January 29 th , 2010, (at the beginning of the lecture) Please justify all of your answers. Write your answer cleanly with sentences and diagrams to explain. Don’t forget to write your name on your copy to receive credit. Problem 1 (20pts): On a two-stage rocket Solve problem 11.1 page 686 of the textbook (new edition). The problem is about a 2-stage, solid-propellant sounding rocket with a delay between burnout. The goal is to compute the maximum altitude reached (similar to the example solved during the last discussion). Problem 2 (30pts): Meditation on forces applied to a rocket 1. Recall the the acceleration of drag on an object moving in a body of air is given as vector a D = 1 2 .ρ.C D . A m . vector V r | vector V r | , where ρ is the air density, C D the non-dimensional drag coefficient,
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Unformatted text preview: A m the area-to-mass ratio and v V r the relative velocity of the air. That is, v V r = v V air-v V rocket . This formula is a priori de²ned relative to an inertial frame. However, show that it is the same in a rotating frame (that is with velocitied computed in a rotating frame). 2. Similarly we derive the equation for thrust:-dm dt v V e relative to an inertial frame of reference. Here v V e is the velocity of the exhaust gas relative to the rocket velocity. Does this velocity depends on the frame in which it is measured? 3. Write down the equations of the rocket in an Earth centered inertial frame and an Earth centered ²xed frame including (non-constant) gravitation, thrust and drag . Explicit the initial conditions. 1...
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