Question 1174200
.
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!)
~~~~~~~~~~~~~~



<pre>
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  {{{2500/64}}}  and the corresponding ratio of squares of times  {{{(t/2)^2}}},

where "t" is the unknown value under the problem's question.


Then you equate these two ratios and get the equation


    {{{2500/64}}} = {{{t^2/4}}}.


From the equation,  {{{t^2}}} = {{{(4*2500)/64}}};  hense  t = {{{(2*50)/8}}} = {{{100/8}}} = 12.5  seconds.


Doing in this way, you get the answer MENTALLY, even without using a calculator (!)


<U>CHECK, using the formula from Physics</U>.  H = {{{(g*t^2)/2}}} = {{{(32*12.5^2)/2}}} = 2500  feet.  (Precisely correct).
</pre>

Solved.


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


Probably, &nbsp;some tutors will show you another way with variations . . . 


I prefer this short method, &nbsp;and I want to get you acquainted with it, &nbsp;because in the school

nobody and never will tell you about it : &nbsp;&nbsp;it is how the &nbsp;US &nbsp;educational system works in Math.