Concept explainers
(a)
To find: The total distance a ball falls in 6 s.
(a)
Answer to Problem 66E
The total distance a ball falls in 6 s is 576 ft.
Explanation of Solution
The distance is increasing with every second.
Here the arithmetic regression is increasing.
Given:
Distance covered by freely falling ball in the first second is 16 ft.
Distance covered by freely falling ball in the next second is 48 ft
Distance covered by freely falling ball in the next second is 80 ft
Total time is 6 s.
Formulas used:
The nth partial sum of an arithmetic sequence is,
Calculation:
Due to the gravitational pull the ball falls with different distance in every second.
In the first second ball falls 16 ft.
So, first term of an arithmetic progression is 16.
In the next second ball falls 48 ft.
So, second term of an arithmetic progression is 48.
And in the next second ball falls 80 ft.
So, third term of an arithmetic progression is 80.
Hence, an arithmetic sequence is formed,
The common difference is calculated as,
So the common difference is 32.
And total time is 6 s, so, value of n is 6.
Substitute 16 for a, 32 for d and 6 for n in equation (1) to find the total distance a ball falls in 6 s.
Thus, the total distance a ball falls in 6 s is 576 ft.
(b)
To find: A formula for the total distance a ball falls in n seconds.
(b)
Answer to Problem 66E
The formula for the total distance a ball falls in n seconds is
Explanation of Solution
Given:
Distance covered by freely falling ball in the first second is 16 ft.
Distance covered by freely falling ball in the next second is 48 ft
Distance covered by freely falling ball in the next second is 80 ft
Calculation:
The first term of an arithmetic progression is denoted by a and the common difference is denoted by d.
The sum for an arithmetic progression is denoted by
Now the total distance a ball falls in n seconds is calculated by adding all the distance covered by the ball in each second.
Thus, the formula for the total distance a ball falls in n seconds is
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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