I am pushing my friend on a swing, every time that it swings back and forth the amount it swings decreases by 30%. The first time I pushed my friend the swing traveled 12 feet. How many times will it take for the distance that they travel to turn into 0?

Note: This is an interesting question since I know the exponential function is equal to 12 x (0.7) ^ (x-1)

I think that it can't get to 0 but I do know that swings do stay still.

Am I considering this problem to deeply?

Thanks!

breadstickim01 Sep 15, 2023

#1**+1 **

It will (theoretically) travel

12 / ( 1 - .7) = 12 / (3/10) = (12 * 10) / 3 = 40 ft

However....if we set the sum of an infinite geometric series to 40

12 [ 1 - .7^r ] / [ 1 - .7 ] = 40

12 [ 1 - .7^r ] / .3 = 40

12 [ 1 - .7^r ] = 12

1 - .7^r = 1

-.7^r = 0

Which means that the number of times (r) that it takes to get the swing to stop is not determinable......however, with friction involved it will eventually stop

CPhill Sep 16, 2023