The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far wi...
Question 1 Report
The distance, d, through which a stone falls from rest varies directly as the square of the time, t, taken. If the stone falls 45cm in 3 seconds, how far will it fall in 6 seconds?
Answer Details
The problem can be solved using the formula for direct variation:
d = kt^2
where d is the distance, t is the time, and k is the constant of variation.
We can solve for k using the given information that the stone falls 45cm in 3 seconds:
45 = k(3)^2
45 = 9k
k = 5
Now that we know k, we can use the formula to find how far the stone will fall in 6 seconds:
d = 5(6)^2
d = 5(36)
d = 180cm
Therefore, the answer is 180cm.
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