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3. Luke and Leia are participating in a space race. Let F(t) be the position of Luke and Leia at time t. At t= 0 (when the race begins) their ship is at the origin, traveling with speed 1 in the direction of the positive z-axis. Their acceleration at time t is given by: ä(t)=< cos(t), sin(2t),8> a. Given that F(t) is the position vector, what is F(0)? b. What is F '(0) = v(0)? c. Find v(t). d. Find F(t).

3. Luke and Leia are participating in a space race. Let F(t) be the position of Luke and Leia at time t. At t= 0 (when the race begins) their ship is at the origin, traveling with speed 1 in the direction of the positive z-axis. Their acceleration at time t is given by: ä(t)=< cos(t), sin(2t),8> a. Given that F(t) is the position vector, what is F(0)? b. What is F '(0) = v(0)? c. Find v(t). d. Find F(t).

Advanced Engineering Mathematics
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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3. Luke and Leia are participating in a space race. Let F(t) be the position of Luke and Leia at time t. At t= 0 (when the race begins) their ship is at the origin, traveling with speed 1 in the direction of the positive z-axis. Their acceleration at time tis given by: ä(t)=<cos(t), sin(2t),8> a. Given that F(t) is the position vector, what is F(0)? b. What is F'(0) = v(0)? c. Find v(t). d. Find F(t).
Transcribed Image Text:3. Luke and Leia are participating in a space race. Let F(t) be the position of Luke and Leia at time t. At t= 0 (when the race begins) their ship is at the origin, traveling with speed 1 in the direction of the positive z-axis. Their acceleration at time tis given by: ä(t)=<cos(t), sin(2t),8> a. Given that F(t) is the position vector, what is F(0)? b. What is F'(0) = v(0)? c. Find v(t). d. Find F(t).
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