i. Explain why the time taken for the player to get to the exit gate is given by T = x² + y² V1 + √(x − x)² + (Y - y)² V2 ii. The player wishes to choose point B on the boundary in order to minimise the total travel time from point A to point C. Use calculus to show that, for this quickest trajectory, the angle 02 depends on 0₁ according to the relation sin 0₁ V1 = sin 02 V₂
i. Explain why the time taken for the player to get to the exit gate is given by T = x² + y² V1 + √(x − x)² + (Y - y)² V2 ii. The player wishes to choose point B on the boundary in order to minimise the total travel time from point A to point C. Use calculus to show that, for this quickest trajectory, the angle 02 depends on 0₁ according to the relation sin 0₁ V1 = sin 02 V₂
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:3.
EVE Online is a space-based multiplayer game, where players use space-
ships to engage in combat, industry, exploration and other activities.
(a)
A player is seeking to travel from her current position in a combat
arena to the exit gate. The gate is located inside a cloud of gas, which is
bounded by a plane: inside this gas, the ship's speed increases from ₁ to V₂.
The diagram below explains the situation: she will travel from point A to point
C by way of point B. (You may assume that any changes in speed or direction
are instantaneous.)
с
0₂
X - X
B
0₁
X
A
Y-y
y
Transcribed Image Text:i.
Explain why the time taken for the player to get to the exit
gate is given by
T =
=
x² + y² √(x − x)² + (Y− y)²
V1
V2
ii.
The player wishes to choose point B on the boundary in order
to minimise the total travel time from point A to point C. Use calculus to
show that, for this quickest trajectory, the angle 0₂ depends on 0₁ according
to the relation
sin 0₁
V1
sin 02
V2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
