SOLUTION: The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 fee
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Question 128636: The distance an object falls is directly proportional to the square of the time it has been falling. After 6 seconds it has fallen 1296 feet. How long will it take to fall 2304 feet? Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Since you are told that the distance (call it D) that an object falls is directly proportional
to the square of the time (let T represent the time), then you can write the proportional
relationship as:
.
.
in which K is the constant of proportionality that makes the equation balance.
.
For this problem we first need to find K. The problem tells you that when T = 6 seconds,
then D = 1296 feet. Substituting these two values into the equation results in:
.
.
Square the 6 and the equation becomes:
.
.
Solve for K by dividing both sides of the equation by 36 and you get:
.
.
and after you do the division you have:
.
.
Now return to the original equation for this falling body:
.
.
and substitute 36 for K to change the equation to:
.
.
From this you can compute the total time it will take to fall a distance of 2304 feet by
substituting 2304 for D in the equation to get:
.
.
Divide both sides of this equation by 36 and you then have:
.
.
Solve for T by taking the square root of both sides to find that:
.
.
This tells you that 8 seconds from the time that object is released it has fallen a
distance of 2304 feet.
.
Hope this helps you to understand what is meant by "is directly proportional to" as well as the
details of solving this problem.
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