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Alexxx [7]
3 years ago
14

A ball was dropped from a height of 60m. Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped. Ho

w far had the ball travelled when it hit the ground for the fifth time?
Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answer:

The ball traveled 116.25 m when it hit the ground for the fifth term

Step-by-step explanation:

This is a geometric progression exercise and what we are asked to look for is the sum of a GP.

The ball was dropped from a height of 60 m. This means that the initial height of the ball is 60 m.

First value, a = 60

Each time it hit the ground, it bounced up 1/2 (half) of the height that it dropped.

This is the common ratio, r = 1/2 = 0.5

The number of terms it hits the ground is the number of terms in the GP.

number of terms, n = 5

The distance traveled by the ball when it hit the ground for the fifth term will be modeled by the equation:

S_n = \frac{a(1 - r^n) }{1 - r} \\S_5 =  \frac{60(1 - 0.5^5) }{1 - 0.5}\\S_5 =  \frac{58.125}{0.5} \\S_5 = 116.25 m

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