Find Height of Elevator at T_1: K&K Q1.17

[Radarithm]

Homework Statement

At t = 0, an elevator departs from the ground with uniform speed. At time T_1 a child drops a marble through the floor. The marble falls with uniform acceleration g = 9.8 m/s², and hits the ground T_2 seconds later. Find the height of the elevator at time T_1

Homework Equations

\frac{dv}{dt}=g
\dot{y}=g\int dt
y=g\int_{T_1}^{T_2}t dt=g\left(\frac{T_2^2-T_1^2}{2}\right)+y_0
y=g\int_0^{T_2}t dt=\frac{gT_2^2}{2}+y_0

The Attempt at a Solution

I was sure of the fact that if I set the 3rd equation above to equal zero, I could solve for the initial height; the problem seemed confusing at first but is actually quite trivial. I turned to the back of the book to look for the answer (and I was sure that I was correct), but I got a hint; if T_1=T_2=4 s then h=39.2 m
The 3rd equation gave me zero, and the fourth one gave me 79.4 m or 2h. I was able to use this to solve for the velocity of the elevator, but that doesn't seem to help much. I'm not sure what I'm doing wrong; the height at T_1 is y_0. Can someone help me out? This should have been so much easier. I've got to be making some mistake in the calculus.

 

[wakefield]

When the marble is dropped its initial velocity is the same as the elevator's velocity upwards.

 

[Radarithm]

edit: nevermind.

 

[jbunniii]

Be careful about the times. The marble is dropped at time $T_1$ and it hits the floor $T_2$ seconds later, i.e. at time $T_1 + T_2$.