Question

A free falling object increases speed by a little over 22 miles per hour each second. The arithmetic sequence 22,44,66 represents the speed after each second, in miles per hour, of a dropped object. How fast is a rock falling after 8 seconds if it dropped over the side of a cliff.

Answer 1

The rock falling after 8 seconds if it dropped over the side of a cliff is 176 miles per hour

Solution:

Given that, A free falling object increases speed by a little over 22 miles per hour each second

The arithmetic sequence that represents the speed after each second in miles per hour of a dropped object is given as:

22, 44, 66

Let us find the common difference between the terms

44 - 22 = 22

66 - 44 = 22

Thus the common difference between the terms is constant

The nth term of arithmetic sequence is given as:

`a_n=a_1 + (n-1)d`

`a_n` = the nᵗʰ term in the sequence

`a_1` = the first term in the sequence

d = the common difference between terms

Here, in the given sequence, 22, 44, 66

`a_1 = 22 \text{ and } d = 22`

`a_n = 22 + (n-1)22\\\\a_n = 22 + 22n - 22\\\\a_n = 22n`

How fast is a rock falling after 8 seconds if it dropped over the side of a cliff

Substitute n = 8 and find the value

`a_8 = 22 * 8 = 176`

Thus the rock falling after 8 seconds if it dropped over the side of a cliff is 176 miles per hour