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?
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