I need help solving this problem

Question

The time it takes a pendulum to complete one period (one swing over and back)
vaires directly with the square root of its length. If a pendulum is 20 feet long and has a
period of 5 sec, find the period of a pendulum that is 30 feet long

Answer 1

The pendulum's period of swing is directly proportional to the square root of the length of the pendulum. Longer pendulum, longer period. So you proportionate the square root of the pendulums lengths:

 

SqRt (30/20) = SqRt (1.5) = 1.225

 

then multiply the 5 second period for the 20 ft pendulum times this value:

 

5 x 1.225 = 6.12 seconds.

Answer 2

20 ft has 5 sec period. 

You want to find the period for 1 ft. 

5/(sq.root 20) = 5/(2 sq.root 5) seconds per foot. 

Multiply by square root of 30 feet. 

You should get (5/2)•(sq.root 6) which is about 6.12 seconds.