A ball is dropped from a height of 1 metre. At every bounce it travels half of the height it travelled it with the previous flight. Find the total distance travelled when the ball comes to rest.
s = a/(1-r) = 1/(1 - 1/2) = 2
A ball is dropped from a height of 1 metre, it bounces back up 2/3 of the previous height, after hitting the ground for the 8th time, what is the total distance of travelled
To find the total distance travelled by the ball, we can sum up the distances it travels during each bounce. Each bounce consists of two phases: going up and coming down.
Let's analyze the distances traveled during each phase on each bounce:
1. Going Up:
- The ball starts at a height of 1 meter and travels half the distance on each bounce. So, during the first bounce, it reaches a height of 0.5 meters.
- In the second bounce, the ball starts from a height of 0.5 meters and reaches a height of 0.25 meters.
- This pattern continues, with each bounce reaching half the height of the previous bounce.
2. Coming Down:
- The distance traveled during the descent is equal to the distance traveled during the ascent.
- So, the distance traveled during the descent will also follow the same pattern as the ascent.
Now, let's calculate the total distance traveled by summing up the distances during each phase on each bounce.
First, let's calculate the total distance during the ascent:
1 + 0.5 + 0.25 + 0.125 + ...
This is a geometric series with a common ratio of 1/2 and a first term of 1. The sum of a geometric series can be calculated using the formula:
Sum = (first term) / (1 - common ratio)
In this case, the sum of the geometric series for the ascent is:
Sum = 1 / (1 - 1/2)
Simplifying this expression, we get:
Sum = 1 / (1/2)
Sum = 2
So, the total distance traveled during the ascent is 2 meters.
Since the distance traveled during the descent is the same as the ascent, the total distance traveled during the descent is also 2 meters.
Therefore, the total distance traveled by the ball when it comes to rest is:
Total Distance = Distance during Ascent + Distance during Descent
= 2 + 2
= 4 meters.
Hence, the ball will travel a total distance of 4 meters before coming to rest.