Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Total distance travelled by a ball.

"A ball is dropped from 10 height. Each time it strikes the ground it bounces vertically to a height equal to 3/4 of the preceding height. What is the total distance traveled by the ball?

So I tried to set this up such that when the ball is dropped, thats 10 meters traveled, it bounces up 3/4 of the way so thats (3/4)10 meters travelled etc etc etc. So it looks like an infinite series such as

x = 10 + 10(3/4) + 10(3/4)^2 + 10(3/4)^3 + ...

in which a = 10 and r = 3/4 so by using the Sn formula I get = 40 meters...but the solutions manual says otherwise. What did I do wrong?

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Total distance travelled by a ball.

After the 10m, the ball bounces up 10(3/4)m and then back down 10(3/4)m etc - you have only taken into account the upwards distances. So you need to double the sum (excluding the 10m) and then add 10m. The answer should be 70m.

Last edited by Daniel123 (2008-03-24 10:22:48)

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: Total distance travelled by a ball.

Ahhh yes. Your a genius!

Thanks.