Typical backyard ants often create a network of chemical trails for guidance. Extending outward from the nest, a trail branches (bifurcates) repeatedly, with 60° between the branches. If a roaming ant chances upon a trail, it can tell the way to the nest at any branch point: if it is moving away from the nest, it has two choices of path requiring a small turn in its travel direction, either 30° leftward or 30° rightward. If it is moving toward the nest, it has only one such choice. The figure below shows a typical ant trail, with lettered straight sections of 1.88 cm length and symmetric bifurcation of 60°. Path v is parallel to the y axis. т п B d. If an ant enters the trail at point A, find the following. (a) the magnitude of the ant's displacement from the nest (find it in the figure) cm (b) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest ° counterclockwise from the +x-axis If an ant enters the trail at point B, find the following. (c) the magnitude of the ant's displacement from the nest cm (d) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest ° counterclockwise from the +x-axis
Typical backyard ants often create a network of chemical trails for guidance. Extending outward from the nest, a trail branches (bifurcates) repeatedly, with 60° between the branches. If a roaming ant chances upon a trail, it can tell the way to the nest at any branch point: if it is moving away from the nest, it has two choices of path requiring a small turn in its travel direction, either 30° leftward or 30° rightward. If it is moving toward the nest, it has only one such choice. The figure below shows a typical ant trail, with lettered straight sections of 1.88 cm length and symmetric bifurcation of 60°. Path v is parallel to the y axis. т п B d. If an ant enters the trail at point A, find the following. (a) the magnitude of the ant's displacement from the nest (find it in the figure) cm (b) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest ° counterclockwise from the +x-axis If an ant enters the trail at point B, find the following. (c) the magnitude of the ant's displacement from the nest cm (d) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest ° counterclockwise from the +x-axis
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Typical backyard ants often create a network of chemical trails for guidance. Extending outward from the nest, a trail branches (bifurcates) repeatedly, with 60° between the branches. If a roaming ant
chances upon a trail, it can tell the way to the nest at any branch point: if it is moving away from the nest, it has two choices of path requiring a small turn in its travel direction, either 30° leftward or
30° rightward. If it is moving toward the nest, it has only one such choice. The figure below shows a typical ant trail, with lettered straight sections of 1.88 cm length and symmetric bifurcation of 60°.
Path v is parallel to the y axis.
т
п
B
d.
If an ant enters the trail at point A, find the following.
(a) the magnitude of the ant's displacement from the nest (find it in the figure)
cm
(b) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest
° counterclockwise from the +x-axis
If an ant enters the trail at point B, find the following.
(c) the magnitude of the ant's displacement from the nest
cm
(d) the angle (relative to the positive direction of the superimposed x axis) of the ant's displacement from the nest
° counterclockwise from the +x-axis
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