How High is the Cliff if a Rock Takes 3.4 Seconds to Hit the Ground?

[Libohove90]

Homework Statement

A rock falls of the cliff, 3.4 seconds later, you can hear the rock hitting the ground. Assuming the speed of sound is 340 m/s, how high is the cliff?

Homework Equations

Delta X = Vot + 0.5at^2
2a Delta X = V^2 - Vo^2

The Attempt at a Solution

I don't know how to start. The height of the cliff is unknown and the time it took the rock to hit the ground is unknown. Initial velocity is zero and that's all I can say. I don't know where to start. Perhaps I am missing something.

 

[kjohnson]

The first thing you need to do is quantify your total time 't' as the sum of the time it takes for the rock to fall 'tf' plus the time it takes for the sound to travel back 'ts' or t=tf+ts. Then you need to use your position equation h(t) where h(tf)=...

 

[Libohove90]

The first thing you need to do is quantify your total time 't' as the sum of the time it takes for the rock to fall 'tf' plus the time it takes for the sound to travel back 'ts' or t=tf+ts. Then you need to use your position equation h(t) where h(tf)=...

Ok so tf + ts = 3.4 s

Position equation of the tf would be $$\Delta$$y = Vo tf + 1/2 atf^2

Position equation of ts would be $$\Delta$$y = v ts (where v = 340 m/s)

Correct?

 

[kjohnson]

Yes, that is pretty much correct. The only thing is your delta y is really height as a function of time or y(t)=vo*t+1/2a*t^2 so when you sub in your total fall time 'tf' you are implying that your height is zero. To get the 'tf' term to sub into that function use the relation t=tf +ts or tf=t-ts. Now you just need your relation of the height of the cliff and the velocity of sound to sub in for 'ts'.

 

[rwisz]

As a scientist, it is important to approach problems with a systematic and logical approach. In this case, we can use the given information and equations of motion to solve for the height of the cliff.

First, let's define our variables:
- t = time (in seconds)
- g = acceleration due to gravity (9.8 m/s^2)
- v = final velocity (in this case, the speed of sound, 340 m/s)
- h = height of the cliff (in meters)

Using the first equation, we can rearrange it to solve for h:
h = 0.5gt^2

Next, we can use the second equation to solve for t:
2aΔx = v^2 - v0^2
2(9.8)(h) = (340)^2 - 0^2
19.6h = 115600
h = 5897.96 meters

Therefore, the height of the cliff is approximately 5897.96 meters. It is important to note that this is assuming the rock was dropped from rest and there were no air resistance. If these factors were present, the calculation would be different. Additionally, it is always important to double check your units and make sure they are consistent throughout the calculation.