Question: The time of a pendulum′s swing varies directly with the square root of its length. If the pendulum is 1 ft long when the time is 0.2 second, find the time if the length is 9 ft.
A ) 0.6 second B ) 1.8 seconds C ) 15 seconds D ) 0.8 seconds
Steps to derive
1 Let t = the time and L = the length
1 Let t = the time and L = the length
2 The time of a pendulum′s swing varies directly with the square root of its length. i.e. t = kL
2 The time of a pendulum′s swing varies directly with the square root of its length. i.e. t = kL
3 Substitute t = 0.2 sec and L = 1 ft in t = kL. 0.2 = k1 k = 0.21 = 0.2
3 Substitute t = 0.2 sec and L = 1 ft in t = kL. 0.2 = k1 k = 0.21 = 0.2
4 Now we need to find the time, if the length (L) is 9 ft. t = (0.2)9 = (0.2)(3) = 0.6
4 Now we need to find the time, if the length (L) is 9 ft. t = (0.2)9 = (0.2)(3) = 0.6
5 If the pendulum is 9 ft long then the time is 0.6 second.
5 If the pendulum is 9 ft long then the time is 0.6 second.
