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:
[tex]a_n=a_1 + (n-1)d[/tex]
[tex]a_n[/tex] = the nᵗʰ term in the sequence
[tex]a_1[/tex] = the first term in the sequence
d = the common difference between terms
Here, in the given sequence, 22, 44, 66
[tex]a_1 = 22 \text{ and } d = 22[/tex]
[tex]a_n = 22 + (n-1)22\\\\a_n = 22 + 22n - 22\\\\a_n = 22n[/tex]
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
[tex]a_8 = 22 \times 8 = 176[/tex]
Thus the rock falling after 8 seconds if it dropped over the side of a cliff is 176 miles per hour
