Concept explainers
Deviation of a Laser Beam A laser beam is to be directed toward the center of the moon, but the beam strays 0.5° from its intended path.
- (a) How far has the beam diverged from its assigned target when it reaches the moon? (The distance from the earth to the moon is 240,000 mi.)
- (b) The radius of the moon is about 1000 mi. Will the beam strike the moon?
a.
To find: The distance of the beam diverse from its assigned target to reach the moon.
Answer to Problem 49E
Distance of the beam diverse from its target to reach the moon is
Explanation of Solution
Given:
The direction of the laser beam is towards the center of the moon.
Distance of earth and moon is
Consider the above figure (1) to calculate the value of
Formula Used:
Trigonometry property of tangent is
Calculation:
The below figure represents the direction of laser beam towards moon.
Let
The value of d is calculated as follows,
Substitute
Therefore, the distance of the beam diverse from its assigned target to reach the moon is
b.
To find: Whether the beam strike the moon or not.
Answer to Problem 49E
The beam will not strike the moon.
Explanation of Solution
Calculation:
The direction of the laser beam is towards the center of the moon.
Distance of earth and moon is
Radius of moon is
And from part (a) the distance of the beam diverse from its assigned target to reach the moon is
The radius of moon is
Then, the beam will not strike the moon.
Chapter 6 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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