You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on in an arithmetic sequence. What is the total distance the object fall in 6 seconds?
distance = 16t^2
when t = 6
distance = 16(6^2) = 576 ft
btw, It might be a federal offense to drop a coin into the Grand Canyon.
To find the total distance the object falls in 6 seconds, we need to sum up the distances the object falls during each second.
We are given that the distance the object falls follows an arithmetic sequence where the common difference between consecutive terms is 32 feet (difference between 48 feet and 16 feet). The first term is 16 feet.
We can use the formula for the sum of an arithmetic sequence to find the total distance:
Sum = (n/2)(2a + (n-1)d)
Where:
- n is the number of terms in the sequence (which is 6 in this case)
- a is the first term (which is 16 feet)
- d is the common difference (which is 32 feet)
Let's plug in the values and calculate the sum:
Sum = (6/2)(2 * 16 + (6-1) * 32)
= (3)(32 + 5 * 32)
= (3)(32 + 160)
= (3)(192)
= 576 feet
Therefore, the total distance the object falls in 6 seconds is 576 feet.
To find the total distance the object falls in 6 seconds, we can use the formula for the sum of an arithmetic sequence.
The first term, a, is 16 feet, and the common difference, d, is 48 - 16 = 32 feet.
The number of terms, n, is 6.
The formula for the sum of an arithmetic sequence is:
Sn = n/2 * (2a + (n-1) * d)
Let's substitute the given values into the formula:
Sn = 6/2 * (2 * 16 + (6-1) * 32)
= 3 * (32 + 5 * 32)
= 3 * (32 + 160)
= 3 * 192
= 576 feet
Therefore, the total distance the object falls in 6 seconds is 576 feet.