A rocket starts at rest at r=0 with initial mass consisting of a payload of mass M together with fuel of mass 9M. The fuel is burnt at a constant rate with the mass being emitted backwards at speed u relative to the rocket. Let (1) be the rocket's speed at time and consider the situation of constant gravitational force (of magnitude g per unit mass) but negligible air resistance. 1. Find the differential equation satisfied by . 2. The rocket will only leave the ground if the rate of fuel burning & is greater than a critical value A. Determine an expression for A, in terms of M. g. and u. λ = 3. Assuming the rocket is able to leave the ground, what is its final velocity y at the time when all the fuel is burnt? 0₁ =

A rocket starts at rest at r=0 with initial mass consisting of a payload of mass M together with fuel of mass 9M. The fuel is burnt at a constant rate with the mass being emitted backwards at speed u relative to the rocket. Let (1) be the rocket's speed at time and consider the situation of constant gravitational force (of magnitude g per unit mass) but negligible air resistance. 1. Find the differential equation satisfied by . 2. The rocket will only leave the ground if the rate of fuel burning & is greater than a critical value A. Determine an expression for A, in terms of M. g. and u. λ = 3. Assuming the rocket is able to leave the ground, what is its final velocity y at the time when all the fuel is burnt? 0₁ =

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A rocket starts at rest at r=0 with initial mass consisting of a payload of mass M together with fuel of mass 9M. The fuel is burnt at
a constant rate with the mass being emitted backwards at speed u relative to the rocket. Let (1) be the rocket's speed at time I and
consider the situation of constant gravitational force (of magnitude g per unit mass) but negligible air resistance.
1. Find the differential equation satisfied by .
de
2. The rocket will only leave the ground if the rate of fuel burning & is greater than a critical value A Determine an expression for
A, in terms of M. g. and u.
d. =
3. Assuming the rocket is able to leave the ground, what is its final velocity uy at the time when all the fuel is burnt?
v₁ =

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