SOLUTION: 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 wil

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(52781) (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!)
~~~~~~~~~~~~~~

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.

------------

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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