A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation m du ck-mg where g is the acceleration due to gravity. (a) Find (t) keeping in mind that the mass m is a function of t. v(t) = In(m/(m(-kt))-9.8t (b) Suppose that the fuel accounts for 50% of the initial mass of the rocket and that all of the fuel is consumed at 140 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.] v(140) = 753 m/sec [Round to nearest whole number] m/sec
A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation m du ck-mg where g is the acceleration due to gravity. (a) Find (t) keeping in mind that the mass m is a function of t. v(t) = In(m/(m(-kt))-9.8t (b) Suppose that the fuel accounts for 50% of the initial mass of the rocket and that all of the fuel is consumed at 140 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.] v(140) = 753 m/sec [Round to nearest whole number] m/sec
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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![A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel).
Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is
being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the
fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the
rocket will satisfy the equation
m
du
dt
=ck - mg
where g is the acceleration due to gravity.
(a) Find (t) keeping in mind that the mass m is a function of t.
v(t) = In(m/(m(-kt))-9.8t
m/sec
(b) Suppose that the fuel accounts for 50% of the initial mass of the rocket and that all of the fuel
is consumed at 140 s. Find the velocity of the rocket in meters per second at the instant the fuel is
exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]
v(140) = 753
m/sec [ Round to nearest whole number]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb712ee53-cda4-4fbf-9bf4-6842d273aff4%2F2e734416-d4bd-4dbf-8b2c-7a939c26d8c3%2Fw4nz4c_processed.png&w=3840&q=75)
Transcribed Image Text:A rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel).
Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is
being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the
fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the
rocket will satisfy the equation
m
du
dt
=ck - mg
where g is the acceleration due to gravity.
(a) Find (t) keeping in mind that the mass m is a function of t.
v(t) = In(m/(m(-kt))-9.8t
m/sec
(b) Suppose that the fuel accounts for 50% of the initial mass of the rocket and that all of the fuel
is consumed at 140 s. Find the velocity of the rocket in meters per second at the instant the fuel is
exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]
v(140) = 753
m/sec [ Round to nearest whole number]
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