Concept explainers
(a)
To find: The length of the arc of the 10th swing.
(a)
Answer to Problem 85AYU
Explanation of Solution
Given: Initially, a pendulum swings through an arc of 2 feet. On each successive, the length of the arc is 0.9 of the previous length.
Initial length of the pendulum = 2 feet.
After each swing loose 0.1 length of the previous length.
After 1 swing length of arc
After 2 bounce height of ball
After 10 bounce height of ball
(b)
To find: The length of arc less than 1 foot.
(b)
Answer to Problem 85AYU
Explanation of Solution
Given: Initially, a pendulum swings through an arc of 2 feet. On each successive, the length of the arc is 0.9 of the previous length.
Initial height of the ball,
After each bounces up loose one-fourth height of the previous one.
Length of arc after nth swung
Length is less than 1 foot.
Before 7 swung length of arc less than 1 foot.
(c)
To find: The number of bounce when height is less than 6 inches.
(c)
Answer to Problem 85AYU
Explanation of Solution
Given: Initially, a pendulum swings through an arc of 2 feet. On each successive, the length of the arc is 0.9 of the previous length.
Initial height of the ball,
Length of arc after nth swung
Put n=15
Length of arc after 15th swung
(d)
To find: The total length when stops swung.
(d)
Answer to Problem 85AYU
Explanation of Solution
Given: Initially, a pendulum swings through an arc of 2 feet. On each successive, the length of the arc is 0.9 of the previous length.
Initial height of the ball,
Length of arc after nth swung
Total length
Hence, total length of arc before its stops is
Chapter 12 Solutions
Precalculus Enhanced with Graphing Utilities
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