Answered: 3. The straight-line distance from…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

200 years has passed and now it is year 2220. The Earth is out of basic resources
as they have been drastically drained in the past 200 years. The president of the
United World Council (UWC) has approved you and your crew’s Mission to
Mars. You will pilot the most advanced spaceship the world has ever known, the
Excelsior! It will carry equipment that will help to transform Mars so as to
resemble the Earth, especially so that it can support human life.
Before the mission can launch a few items need to be figured out. What is the
capacity of the fuel tank? How long should the fuel burn to achieve escape
velocity (otherwise the Excelsior will be stuck in the Earth’s gravitational pull)?
How long will it take the Excelsior to arrive at Mars?

3. The straight-line distance from Earth to Mars at the time the launch is
scheduled is 100 million miles. In order to avoid other celestial bodies the
Excelsior must travel in an arc given by the equation
y =
(x – 50)² + 20
125
where x and y are in millions of miles, and the x-axis denotes the straight-line
distance to Mars. Find the actual distance travelled by the Excelsior rounded
to the nearest million and then find the approximate time for the trip rounded
to the nearest month, assuming a constant speed of 30,000 mph and 30 days
in
each
month.
(Hint:
Use
Arc
length
formula given by
dy
1+ ² dx
`dx'
%D
a

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