a ball tossed to a height of 4 meters rebounds 40% of its previous height. the total distance travelled by the ball by the time it comes to rest is?

S = a/(1-r) = 4/(1-.4) = 4/.6 = 20/3

a ball tossed to a height of 4 meters rebound to 40% of its previous height.find the total distance traveled by the ball by the time comes to rest?

To find the total distance traveled by the ball by the time it comes to rest, we can break it down into two parts: the upward journey and the downward journey.

Let's begin with the upward journey. The ball is initially tossed to a height of 4 meters. As it rebounds 40% of its previous height, the maximum height it reaches during each rebound will be 40% of the previous height. Therefore, the ball rebounds to a height of 4 * 0.40 = 1.6 meters.

To calculate the total distance traveled during the upward journey, we need to sum up the distances traveled during each rebound until the ball stops reaching a height over 0.1 meters (since 0.1 meters is considered negligible).

The first "bounce" takes the ball from 4 meters to 1.6 meters, covering a distance of 4 - 1.6 = 2.4 meters.

The second "bounce" takes the ball from 1.6 meters to 1.6 * 0.40 = 0.64 meters, covering a distance of approximately 1.6 - 0.64 = 0.96 meters.

The third "bounce" takes the ball from 0.64 meters to 0.64 * 0.40 = 0.256 meters, covering a distance of approximately 0.64 - 0.256 = 0.384 meters.

Using the same pattern, you can continue calculating the distances traveled during each rebound until the height becomes negligible (less than 0.1 meters).

Now, let's move on to the downward journey. The ball starts its downward journey from the highest point it reached during the upward journey, which is 1.6 meters. This distance is covered in a single rebound.

To find the total distance traveled during the downward journey, we can consider it as the sum of distances traveled during each upward rebound, as the pattern of rebounds is symmetric. So, the total distance traveled during the downward journey is the same as the total distance traveled during the upward journey, which we calculated above.

Finally, we can sum up the distances traveled during the upward and downward journeys to find the total distance traveled by the ball. Add up the distances traveled during each rebound on the way up and multiply it by 2, since the upward and downward journeys cover the same distances.

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