a ball falls from a height of 2.4m and bounces from the same spot, each bounces rise to 3/5 the height of the preceeding bounce.
a. write the series of the movement from start to the eighth bounce.
b.Find th etotal distance moved by the ball as indicated in (a) above
c. Find the total distance the ball can move if bounced infinitely.
look at this question
http://www.jiskha.com/display.cgi?id=1327809291
just one number is different.
To find the series of movements from the start to the eighth bounce, we can use the given information that each bounce rises to 3/5 the height of the preceding bounce.
a. The height of each bounce can be calculated by multiplying the previous bounce's height by 3/5.
Let's start with the first bounce:
Bounce 1: Height = 2.4m
Now, for the subsequent bounces, each bounce's height will be 3/5 of the previous bounce's height:
Bounce 2: Height = (3/5) * 2.4m
Bounce 3: Height = (3/5) * [(3/5) * 2.4m]
Bounce 4: Height = (3/5) * [(3/5) * [(3/5) * 2.4m]]
...
Bounce 8: Height = (3/5) * [(3/5) * [(3/5) * [(3/5) * [(3/5) * [(3/5) * [(3/5) * [(3/5) * 2.4m]]]]]]]
To simplify the calculation, we can use a recursive formula:
Bounce n: Height = (3/5) * Height of Bounce (n-1)
Using this formula, we can calculate the height for each bounce until the eighth bounce.
b. To find the total distance moved by the ball, we need to consider both the upward movement and the downward movement for each bounce.
For the upward movement, the distance covered is equal to the height of each bounce.
Now, for the downward movement, the distance covered will be two times the height of each bounce. This is because the ball falls from the maximum height and covers the same distance again for each bounce.
To find the total distance, we need to calculate the cumulative sum of the upward and downward distances for each bounce until the eighth bounce.
c. To find the total distance the ball can move if bounced infinitely, we need to consider that the ball will continue to bounce endlessly.
We can observe that the height of each bounce becomes progressively smaller with each bounce. Eventually, the height of the bounces will become negligible, and the ball will effectively stop bouncing. Therefore, the total distance the ball can move when bounced infinitely will approach the sum of the distances covered in part (b), but it will never actually reach that value.
To calculate the distances and height for each bounce, you can perform the calculations manually or use a spreadsheet or programming software to automate the process.