Question

You gave your little sister a good push on a swing and it made an arc of 12 ft. On the third swing it made an arc of 8.67 ft. How far did it go on the second swing?

Answer 1

10.2 ft Ans.

We solve this using geometric series.

A1 = 12 ft
A2 = ?
A3 = 8.67ft
Now, for geomteric progression,

$\frac{A1}{A2} = \frac{A2}{A3}$


$\frac{12}{A2} = \frac{A2}{8.67}$

$A2 * A2 = (A2)^{2} = \sqrt{12 * 8.67 }$ 
 
A2 = 10.2 ft