Feet Many
Posted By admin on September 7, 2009
Feet Many
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How many feet would an object fall in the tenth second?
Maria drops a stone from the top of a building. The stone falls 4.9 meters in the first second, 14.7 meters in the second second, and 24.5 feet in the third second, regardless of its weight. How many feet would an object fall in the tenth second?
A. 102.9 m
B. 93.1 m
C. 83.3 m
D. 88.2 m
Please explain.
Galileo noticed that when objects fell they gained distance every second in odd number multiples. If the object fell X in the first second, it would fall 3X in the second, 5X in the third, 7X in the fourth, and so on.
So following that pattern, in the nth second it would fall (2n-1)X where X is the distance in the 1st second (or more to the point the 10th odd number is 19)
=(2*10-1)*4.9m =19*4.9m =93.1m (choice B)
Another way to do it, is to use the ideas Newton came up with. The total distance an object falls starting from rest is d = (1/2) g t² where 9.8 m/s² and t is time in seconds. Find out the total distance for 10 seconds and subtract the total distance for 9 seconds.
∆d = d10 - d9 = (1/2) g ((10s)²-(9s)²) = (1/2) g (19s²) = 4.9m x 19 = 93.1m
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