Question

A child on a swing sweeps out a distance of 45 ft on the first pass. If she is allowed to continue swinging until she​ stops, and if on each pass she sweeps out a distance one half of the previous​ pass, how far does the child​ travel?

Answer 1

Answer:

d = 90 ft

Explanation:

Here in each swing the distance sweeps by the swing is half of the initial distance that it will move

So here we can say that total distance in whole motion is  given as

$d = 45 + \frac{45}{2} + \frac{45}{4} + \frac{45}{8}..........$

since it is half of the distance that it will move in each swing so it would be a geometric progression with common ratio of 1/2

so sum of such GP is given by the formula

$S = \frac{a}{1 - r}$

$d = \frac{45}{1 - \frac{1}{2}}$

$d = 90 ft$