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You are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0

You are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0

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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You are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0 c. r'(30) = 120 d. For 60 ≤ t ≤ 64, k(t) = 40 and z is constant. e. For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full rotation in the normal (NB) plane while your T remains constant.
Transcribed Image Text:You are on a rollercoaster, and the path of your body is modeled by a vector function r(t), where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y is N/S, z is height). Explain what the following would represent physically, being as specific as possible. These are all common roller coaster shapes/behaviors and can be explained in specific language with regard to units: a. r(0)=r(120) b. For 0 ≤ t ≤ 30, N(t) = 0 c. r'(30) = 120 d. For 60 ≤ t ≤ 64, k(t) = 40 and z is constant. e. For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full rotation in the normal (NB) plane while your T remains constant.
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