A bouncy ball bounces 16m on its first bounce and then 8m on the second bounce. Each time it bounces the height halves. How high will the ball bounce on the 10th bounce?
it bounces 32/2^n m on the nth bounce.
So, on the 10th bounce, it bounces 32/1024 = 1/32 m
To determine how high the ball will bounce on the 10th bounce, we need to understand the pattern of the heights of each bounce.
The problem states that the ball bounces 16m on the first bounce and then 8m on the second bounce, with each subsequent bounce height halving. This shows us a clear pattern that the height of each bounce follows a geometric sequence with a common ratio of 1/2.
We can use the formula for the nth term of a geometric sequence to find the height of the 10th bounce. The formula is as follows:
an = a * r^(n - 1)
where:
an is the nth term (height of the nth bounce)
a is the first term (height of the first bounce)
r is the common ratio (in this case, 1/2)
n is the number of terms (in this case, 10)
Applying the formula, we have:
a = 16 (height of the first bounce)
r = 1/2 (common ratio)
n = 10 (number of terms)
Using these values in the formula, we can calculate the height of the 10th bounce:
a10 = 16 * (1/2)^(10 - 1)
= 16 * (1/2)^9
= 16 * (1/512)
= 0.03125m
Therefore, the ball will bounce to a height of 0.03125m on the 10th bounce.