5) You are on a rollercoaster, and your path 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. Assume the axes represent the standard cardinal directions and elevation, and the "location" is your center of mass. Explain what the following represent physically, being specific (these are all pretty standard roller coaster shapes/behaviors): а. r(0) %3D r(120) b. For 0
5) You are on a rollercoaster, and your path 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. Assume the axes represent the standard cardinal directions and elevation, and the "location" is your center of mass. Explain what the following represent physically, being specific (these are all pretty standard roller coaster shapes/behaviors): а. r(0) %3D r(120) b. For 0
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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Transcribed Image Text:5) You are on a rollercoaster, and your path 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.
Assume the axes represent the standard cardinal directions and elevation, and the
"location" is your center of mass. Explain what the following represent physically,
being specific (these are all pretty standard roller coaster shapes/behaviors):
а. r(0) %3D r(120)
b. For 0 <t < 25, N(t) = 0
с. T(20)| — 100
d. r(20) = (a, b, 10), r(22) = (a, b + 5, 100), r(24) = (a, b + 10, 10). T(20)
and T(24) are pointing in the positive x, T(22) is pointing in the negative x.
е. For 40 < t< 44, к(t) %3
and z is constant.
25
= -
f. For 60 <t < 63, the osculating circle has a large radius, gets smaller to a
minimum radius of 10, and then starts to get larger again.
g. For 80 <t < 82, your B begins by pointing toward positive z, and does one
full rotation in the normal (NB) plane while your T remains constant.
TT
h. For 100 < t < 104, r(t) = (15 sin (t),20t, – 15cos (t) + 20)
2
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