A lighthouse is located 40 meters off-shore. The beam of light from the lighthouse rotates at a rate of 2 revolutions per minute clockwise. The beam hits a cliff on the beach 60 meters away, producing a dot of light that moves horizontally along this cliff. Let be the angle between the beam and the line through the searchlight perpendicular to the cliff. Use a trig function for the relationship. 7 a. How fast is this light moving along the beach when 8 == if the beam is moving toward the 3 4 perpendicular line? (remember you need radians for trig functions and their derivatives) I b. How fast is this beam moving when =- if the dot is moving away from the perpendicular line? (Adjust picture to have light beam on other side of the vertical) beach/cliff 60m Lighthouse
A lighthouse is located 40 meters off-shore. The beam of light from the lighthouse rotates at a rate of 2 revolutions per minute clockwise. The beam hits a cliff on the beach 60 meters away, producing a dot of light that moves horizontally along this cliff. Let be the angle between the beam and the line through the searchlight perpendicular to the cliff. Use a trig function for the relationship. 7 a. How fast is this light moving along the beach when 8 == if the beam is moving toward the 3 4 perpendicular line? (remember you need radians for trig functions and their derivatives) I b. How fast is this beam moving when =- if the dot is moving away from the perpendicular line? (Adjust picture to have light beam on other side of the vertical) beach/cliff 60m Lighthouse
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:4. A lighthouse is located 40 meters off-shore. The beam of light from the lighthouse rotates at a rate of 2
revolutions per minute clockwise. The beam hits a cliff on the beach 60 meters away, producing a dot of
light that moves horizontally along this cliff. Let be the angle between the beam and the line through
the searchlight perpendicular to the cliff. Use a trig function for the relationship.
T
a. How fast is this light moving along the beach when = if the beam is moving toward the
h
3
perpendicular line? (remember you need radians for trig functions and their derivatives)
b. How fast is this beam moving when
I
if the dot is moving away from the perpendicular
13
line? (Adjust picture to have light beam on other side of the vertical)
beach/cliff
CALCECCO
60m
Lighthouse
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