Trying to solve the ball problem:
Problem:
A ball is dropped 100 feet and bounces straight. On each bounce the ball climbs half of the height of its previous flight. Assume that the ball bounces forever. How far will the ball travel?
Approach:
First of all the question is asking for a distance of how far the ball will travel.
We know that it starts with a 100 feet bounce and every time bounces half of its previous flight.
We also know it bounces forever therefore we might think that the answer is infinity, but remember Sybil and Zeno´s Paradox.
Remember the sum of an infinite geometric Series.
Solution:
Now we can start by listing the first few terms.
Because we know it is going to be half of the previous flight, then:
N= 100, 100/2, (100/2)/2, … or N= 100, 50, 50/2 or simply n= 100,50,25…
But remember it is asking for a sum because how far will the ball travel asks for the sum of all the infinite distances.
So n= 100+ 100/2+…
We know now that t1 must equal 100 feet and r is .5 because the ball bounces 50% or let’s say half of its previous flight.
Then if we apply the Formula, Sum of an Infinite Geometric Series:
Sn = t1/1-r
Solve with plugging in:
Sn = 100/1-.5
=100/.5
=200 feet
Or else it says that the how far will the ball travel is no more or not even reach 200 feet
Subscribe to:
Post Comments (Atom)
1 comment:
Well your approach to the problem is correct but your answer isn't. You simply forgot to add 100 from the first drop. The answer cam't be 200 because the ball travels 200 feet after it bounces once. (First it travels 100 feet when you drop it and then it comes up 50 feet and down 50 feet more, that adds up to 200). You series is correct, you just need to make sure to include every aspect of the problem, in this case you just missed the initial 100 feet drop.
correct answer: 300 feet
Post a Comment