A tennis ball rebounds each time to a height equal to half of the height of previous bounce,if it's first dropped from a height of 8mtrs.Find the total vertical distance it has traveled when it hits ground for the 10 th time
Answers
Answer:
Tennis ball touch down 10 times, and bounce 9 times.
Down ↓ 16, 8, 4, 2, ...
Up ↑ 8, 4, 2, ...
So, we have two geometric sequences, were each number, after the first is twice less than previous. The only difference between them is 16.
Let's find the sum of the numbers of second geometric sequence ( Up )
~~~~~~~~~~~~~~~~~
1 - rn
S9 = a1 • ————
1 - r
a1 is the first term of geometric sequence,
r is the common ratio
n is the number of terms
~~~~~~~~~~~~~~~~~~~~
a1 = 8
r = 1/2
n = 9
1 - (1/2)9
S9 = 8 · —————— =
1 - (1/2)
8 · [ 1 - (1/512) ] ÷ (1/2)
16 · (511 / 512) = 511 / 32
The total distance is twice of "distance Up" and 16
16 + 2 · (511/32) =
16 + (511/16) =
(256/16) + (511/16) =
767/16 = 47.9375 m
Step-by-step explanation:
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a = 8
n = 9
r = 0.5
Sn = a(1-r^n)
-----------
1 - r
S9 = 15.968 m
total distance = 15.968 + 8
= 23.969 m