Falling Object And Sound Takes 3.2sec

[TomFoolery]

Homework Statement

A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 3.2s later. If the speed of sound is 340m/s, how high is the cliff?

V₀= 0
A=-9.8m/s²
T_total=3.2s
T_sound=Y/340
Y₀=Height
Y=0 (height at sea)

Homework Equations

Y=Y₀+V₀T+1/2(-9.8m/s²)T²

becomes

-Y₀=(-4.9m/s²)*(3.2s-(Y₀*s/340))²

The Attempt at a Solution

I have tried many different solutions, none seem to work. I am convinced that my problem lies in the equation above. Many of my answers are imaginary, so I must have a problem with my (3.2-y/340)² part.

It seems to me that it all balances out in units, so it should be an arithmetic problem. Yet, every time I run it, I get different results. My best guess was to try:
(-4.9)(3.2²-(6.4/340)y₀+(1/340²)y₀²)-y₀

 

[p21bass]

It's probably easier to visualize if you set up three equations. One should represent the time it takes for the rock to fall; the second should represent the time it takes for the sound to get back to the top of the cliff; and the third is the total of both times.

 

[Halliday]

TomFoolery:

You appear to have made a sign error in your last equation. The last term should be adding y₀, rather than subtracting it. I get two real answers. (I never put any numbers in, so I don't have a numeric answer. I always use only symbols [with the exception of small integers, like 2], so it is much easier to manipulate.)

David

 

[TomFoolery]

Thanks for your responses, I'll have to try the 3 equation idea and recheck my signs and run both to see if either/both work as I expect them to. This has been driving me nuts.