1. A space-ship is heading towards a planet, following the trajectory, r(t) = (Ae-t² cos(3t), √2Ae-t² sin(3t), -Ae-t² cos(3t)), where A 50,000km and the time is given in hours. (a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does the ship reach the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. = (b) To 4 significant figures and including units, what are the velocity and speed of the space-ship when it reaches the planet?
1. A space-ship is heading towards a planet, following the trajectory, r(t) = (Ae-t² cos(3t), √2Ae-t² sin(3t), -Ae-t² cos(3t)), where A 50,000km and the time is given in hours. (a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does the ship reach the planet? Give your answer (in hours) both as an exact expression and as a decimal correct to 4 significant figures. = (b) To 4 significant figures and including units, what are the velocity and speed of the space-ship when it reaches the planet?
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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![1. A space-ship is heading towards a planet, following the trajectory,
r(t) = (Ae-¹² cos(3t), √2Ae-t² sin(3t), - Ae-t² cos(3t)),
where A 50, 000km and the time is given in hours.
(a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does
the ship reach the planet? Give your answer (in hours) both as an exact expression and as a
decimal correct to 4 significant figures.
(b) To 4 significant figures and including units, what are the velocity and speed of the
space-ship when it reaches the planet?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F390981ff-b929-4204-840e-511423b3948f%2Fc0c73cd1-1a05-4e25-8beb-6e0b26ce0a8a%2Fnuktg1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A space-ship is heading towards a planet, following the trajectory,
r(t) = (Ae-¹² cos(3t), √2Ae-t² sin(3t), - Ae-t² cos(3t)),
where A 50, 000km and the time is given in hours.
(a) The planet is centred at the origin and has a radius, rp = 2,000km. At what time does
the ship reach the planet? Give your answer (in hours) both as an exact expression and as a
decimal correct to 4 significant figures.
(b) To 4 significant figures and including units, what are the velocity and speed of the
space-ship when it reaches the planet?
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