Constant acceleration of velocity

It always helps to draw a picture and free body diagram, then write the equation of motion, and solve for what you want. In this case, you have a rock of mass m, acted upon by gravity g, falling from rest, starting from a height x above the window. What you are given is the time it takes to cover a certain distance during it's fall to the ground. Hope this helps get you thinking in the right direction.

 

Let me try this way. You have an equation of motion that relates distance fallen (from an unknown point above the window) as a function of time. Seems to me a fruitful approach is to express that equation of motion for [itex]x_1, t_1[/itex] and [itex]x_2, t_2[/itex], where [itex]x_1[/itex] represents the top of the window and [itex]x_2[/itex] represents the bottom of the window. Subtracting the 2 equations gives you [itex]x_1 - x_2[/itex], which you know.

 

Had to do a little head scratching. I believe the following will work:

Using the equation of motion of the rock you should be able to get an equation for [itex]x_1-x_2[/itex] in terms of [itex]g[/itex], [itex]t_1^2[/itex] and [itex]t_2^2[/itex]. You know [itex]x_1-x_2[/itex], and [itex]g[/itex], but not [itex]t_1[/itex] or [itex]t_2[/itex]. But, you do know [itex]t1-t2[/itex]. Thus, you have two equations in two unkowns and should be able to solve for [itex]t_1[/itex], back substitute into the equation of motion, and find [itex]x_1[/itex].

 

Were you able to solve it? I got [itex]x_1[/itex] equal to a little over 2m using the above methodology.