2. An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the 2nd second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth second, it falls 112 feet. Assuming this pattern continues, how many feet does the object fall in the first 7 seconds after it is dropped?
Question
- An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the 2nd second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth second, it falls 112 feet. Assuming this pattern continues, how many feet does the object fall in the first 7 seconds after it is dropped?
Solution
The pattern here is that the object falls an additional 32 feet each second.
In the first second, it falls 16 feet. In the second second, it falls an additional 32 feet (for a total of 48 feet). In the third second, it falls an additional 32 feet (for a total of 80 feet). In the fourth second, it falls an additional 32 feet (for a total of 112 feet).
So, to find out how far it falls in the first 7 seconds, we can continue this pattern:
In the fifth second, it falls an additional 32 feet (for a total of 144 feet). In the sixth second, it falls an additional 32 feet (for a total of 176 feet). In the seventh second, it falls an additional 32 feet (for a total of 208 feet).
To find the total distance fallen in the first 7 seconds, we add up these amounts:
16 feet + 48 feet + 80 feet + 112 feet + 144 feet + 176 feet + 208 feet = 784 feet
So, the object falls 784 feet in the first 7 seconds after it is dropped.
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