Solving a Free-Fall Problem with Height & Time

[lolrelativity]

I am wondering if I did this right.

Homework Statement

An object falls a distance h from rest. If it travels 0.57h meters in the last 1.00 s,
I need to know the time and the height of its fall.

Homework Equations

The Attempt at a Solution

Here what I have:

Since it traveled .57H meters in the last second, I used y=vt+.5gt^2, and got .57H=4.9 since the time elapsed is 1 second and it came from rest, so the inital velocity is zero. Then I solved for H, getting around 8.59 m. Then with this I set up 8.59=4.9t^2, and solved for T, getting around 1.325 seconds. Was these the right methods?

 

[HallsofIvy]

Since, as you say, the initial velocity is 0, the distance traveled in t seconds is y= .5gt^2. But he "time elapsed" is NOT 1 second. You are told that the object travels 0.57h m in the last second but you don't know how many seconds it had fallen before that. You are assuming the object fell .57h m in the first second.

Suppose it fell for a total of T seconds. Then it fell .57h meters between T-1 and T. In the first T-1 seconds it fell .5g(T-1)^2 and in all T seconds it fell .5gT^2 meters. During that last second, it fell .5gT^2- .5g(T-1)^2= .57h meters. And, of course, you have .5gT^2= h, the total distance fallen.