Question 78051
note: to write the radical sign {{{sqrt(x)}}} write sqrt(x) and surround it by three { curly brackets on both sides (use the other curly bracket } for the right side) Click "view source" to see what I'm talking about.


To find the time, simply plug in s=1400.

{{{t=(1/4)*sqrt(1400)}}}

If we list all the factors of 1400 we get:


1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400



Notice the largest perfect square is 100, so rewrite 1400 as 100*14

{{{t=(1/4)*sqrt(100*14)}}}


{{{t=(1/4)*sqrt(100)*sqrt(14)}}} Rewrite the equation using {{{sqrt(xy)=sqrt(x)sqrt(y)}}}


{{{t=(1/4)*10*sqrt(14)}}} Reduce


{{{t=(10/4)*sqrt(14)}}} Multiply


{{{t=(5/2)*sqrt(14)}}} Reduce the fraction

So this is the exact time that it takes to fall. The approximate time is about 9.35414 seconds