A quirky math problem about a rubber ball dropping from a specific height?

2*20 + 2*20*.8 + 2*20*.8^2 + ...

= 40/(1-.8)

= 200 ft

Bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce #a million --- (9/10)10 Bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce #2 --- (9/10)(9/10)10 = (9/10)^210 Bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce #3 --- (9/10)(9/10)(9/10)10 = (9/10)^310 Bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce #4 --- (9/10)(9/10)(9/10)(9/10)10 = (9/10)^410 . . . Bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce #gadgets --- (9/10)^b98b3dfbd27e71e6c3ceeae5877b5210 Takb98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52g Lb98b3dfbd27e71e6c3ceeae5877b52m (9/10)^b98b3dfbd27e71e6c3ceeae5877b5210 ab98b3dfbd27e71e6c3ceeae5877b52 gadgets --> ? The lb98b3dfbd27e71e6c3ceeae5877b52mb98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52 evalb98b3dfbd27e71e6c3ceeae5877b52ab98b3dfbd27e71e6c3ceeae5877b52eb98b3dfbd27e71e6c3ceeae5877b52 b98b3dfbd27e71e6c3ceeae5877b52o 0. So, b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52 doeb98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52'gadgets db98b3dfbd27e71e6c3ceeae5877b52verge. Now b98b3dfbd27e71e6c3ceeae5877b52ake b98b3dfbd27e71e6c3ceeae5877b52he SUM: => ?(9/10)^b98b3dfbd27e71e6c3ceeae5877b5210 ab98b3dfbd27e71e6c3ceeae5877b52 gadgets --> ? The b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52m evalb98b3dfbd27e71e6c3ceeae5877b52ab98b3dfbd27e71e6c3ceeae5877b52eb98b3dfbd27e71e6c3ceeae5877b52 b98b3dfbd27e71e6c3ceeae5877b52o ninety [b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52]. Ib98b3dfbd27e71e6c3ceeae5877b52'gadgets prepob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52erob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52 b98b3dfbd27e71e6c3ceeae5877b52hab98b3dfbd27e71e6c3ceeae5877b52 b98b3dfbd27e71e6c3ceeae5877b52he ball wob98b3dfbd27e71e6c3ceeae5877b52ld bob98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ce b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52fb98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52b98b3dfbd27e71e6c3ceeae5877b52ely. Whab98b3dfbd27e71e6c3ceeae5877b52 plab98b3dfbd27e71e6c3ceeae5877b52eb98b3dfbd27e71e6c3ceeae5877b52 do human beings lb98b3dfbd27e71e6c3ceeae5877b52ve ob98b3dfbd27e71e6c3ceeae5877b52 ab98b3dfbd27e71e6c3ceeae5877b52yway? hb98b3dfbd27e71e6c3ceeae5877b52h

Let the height to which the ball is thrown initially be x.

After one bounce the height to which it goes is (80/100)x=x*0.8

After two bounces the height to which it goes is (80/100)(x*0.8)=x*(0.8)^2

Similarly for the 'n'th bounce the ball goes to a height of x*(0.8)^n

And so on till the ball comes to rest.

Total distance travelled by the ball=x+(x*0.8)+(x*0.8^2)+......+(x*0.8^n)+.......infinity

This is a geometric series of the form

a+a*r+a*r^2+....+a*r^n+....

which has a solution a/(1-r) provided that r<1 .If r>1 the answer is infinite

Here,

a=x

and r=0.8

We have that r<1 hence we can apply the above formula,

a/(1-r)=x/(1-0.8)=5*x

Here,

x is given as 20

Hence the total distance travelled by the ball is 5*20=100 feet.(answer)

The

20 + .8(20) + .8(.8(20)) + .8(.8(.8(20)))... and so on. Multiply all by 2 to incorporate round trip.

20(2) + 16(2) + 12.8(2) + 10.24(2) + 8.19(2) + 6.55(2) + 5.24(2) + 4.19(2) + 3.35(2) + 2.68(2) + 2.14(2) + 1.71(2) + 1.37(2) + 1.1(2) + .88(2) + .7(2) + .56(2) + .45(2) + .36(2) + .29(2) + .23(2) + .18(2) + .14(2) + .11(2) + .09(2) + .07(2) + .06(2) + .05(2) + .04(2) + .03(2) + .02(2) + .01(2)

199.66 feet

20+(.8*20)+(0.8*(0.8*20))+.......and it keeps going until the hight of the ball reaches closer to 0....you add all of them up and get an ansswer..