A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time?

Question

anonymous · Answer

It is a G.P....With a = 9  r = 2/3      Sn =  a ( 1-r^n) / (1-r)

anonymous · Answer

thanks!! so how far will it have traveled byt he time it hits the ground for the 4th time in that case?

anonymous · Answer

@Yahoo!

anonymous · Answer

Distance travelled=9+2[9(2/3)+9(2/3)^2+9(2/3)^3 ]=34.33

anonymous · Answer

thank you so much!!

anonymous · Answer

Any time. By the way, if u need 2 find the distance traveled by the time it stops,here's the aswer.

Distance travelled=9+  lim(n→α)⁡ 2[9(2/3)+9(2/3)^2+9(2/3)^3+⋯+〖9(2/3)〗^r+⋯9(2/3)^n ]
=9+18[lim(n→α)⁡ ((1-(2⁄3)^n)/(1-2⁄3)) ]
=9+18[1/(1⁄3)]=9+18*3=63

anonymous · Answer

@chphiranya great, really helped me understand it better, thanks again
the answer to this problem i posted is 34.33 though correct?