a ball is dropped from a height of 5m assuming that on each bounce the ball return to 60percent of its height attained
To solve this problem step-by-step, we can use the information given to determine the height of the ball after each bounce. Here's how we can do it:
Step 1: Determine the initial height:
The ball is dropped from a height of 5m. So, the initial height is 5m.
Step 2: Calculate the height after the first bounce:
After the first bounce, the ball returns to 60% of its height attained. So, after the first bounce, the ball reaches a height of 60% of 5m.
Height after the first bounce = 0.6 x 5m = 3m.
Step 3: Calculate the height after the second bounce:
Again, after the second bounce, the ball returns to 60% of its height attained. So, after the second bounce, the ball reaches a height of 60% of 3m.
Height after the second bounce = 0.6 x 3m = 1.8m.
Step 4: Continue the process for subsequent bounces:
You can continue this process for as long as you want, calculating the height after each bounce by multiplying the previous height by 0.6. Each time, the ball will reach a height that is 60% of the previous height.
So, to sum it up:
- After the first bounce, the ball reaches a height of 3m.
- After the second bounce, the ball reaches a height of 1.8m.
- After the third bounce, the ball reaches a height of 1.08m.
- And so on...
Note that the height will gradually decrease with each bounce, approaching zero but never actually reaching it.
To find the height attained after each bounce, we can use the concept of geometric progression. Geometric progression is a sequence of numbers where the ratio between any two consecutive terms is constant.
In this case, the height after each bounce will be 60% of the previous height. Let's assume the height after the first bounce is h.
Height after the first bounce: h = 5m * 0.6
The height after each subsequent bounce would be: h * 0.6, h * 0.6 * 0.6, and so on.
To find the height after multiple bounces, we can use the formula for the sum of a geometric series:
Sn = a * (1 - r^n) / (1 - r)
Where:
Sn is the sum of the geometric progression after n terms,
a is the first term of the geometric progression,
r is the common ratio between consecutive terms,
n is the number of terms in the geometric progression.
In our case, a = 5m, r = 0.6 and we have to find the sum after n terms.
We need to determine if there are any specific conditions given for the number of bounces. If not, we can generalize the formula to calculate the height after any number of bounces.
Let's say we want to know the height after 5 bounces:
n = 5
Sn = 5m * (1 - 0.6^5) / (1 - 0.6)
Using this formula, we can calculate the height after 5 bounces.
maybe this will get you started.
The height attained after the nth bounce is
5*0.60^n