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.

 

[rwisz]

=0

But that doesn't work either.
Based on the given information and equations, I understand that the problem is to determine the height of the cliff from which a rock was dropped, based on the time it took for the sound of the impact to reach the observer. However, the approach taken in the attempt at a solution is not correct.

The correct equation to use in this scenario is the distance formula:

d = v*t

Where:
d = distance (height of the cliff)
v = speed of sound (340m/s)
t = time (3.2s)

Therefore, the equation to solve for the height of the cliff would be:

d = (340m/s)*(3.2s)
d = 1088m

Therefore, the cliff is approximately 1088 meters high. It is important to note that this is a simplified calculation, as it does not take into account factors such as air resistance and the varying speed of sound with altitude. However, for a basic understanding of the height of the cliff, this calculation should suffice.