Question 1174200: 4. The distance a body falls from rest (neglecting air resistance) varies directly as the square of the time it falls. If an object drops 64 feet in 2 seconds, how many seconds will it take an object to reach the sea if it is dropped from a plane 2500 feet above the sea level? (show complete solution using variations thanks!)
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
The distance a body falls from rest (neglecting air resistance) varies directly as the square of the time it falls.
If an object drops 64 feet in 2 seconds, how many seconds will it take an object to reach the sea if it is dropped from
a plane 2500 feet above the sea level? (show complete solution using variations thanks!)
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There are two ways to solve this problem.
One way (using variations) is long and assumes making a number of unnecessary calculation; so, it is open for making errors.
The other way is short and error's proven.
Going short vay, you make the ratio of distances  and the corresponding ratio of squares of times  ,
where "t" is the unknown value under the problem's question.
Then you equate these two ratios and get the equation
=  .
From the equation,  =  ; hense t =  =  = 12.5 seconds.
Doing in this way, you get the answer MENTALLY, even without using a calculator (!)
CHECK, using the formula from Physics. H =  =  = 2500 feet. (Precisely correct).
Solved.
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Probably, some tutors will show you another way with variations . . .
I prefer this short method, and I want to get you acquainted with it, because in the school
nobody and never will tell you about it : it is how the US educational system works in Math.
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