Calculating Cliff Height from Sound Time Delay | Kinematics Question

[Intr3pid]

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 340 m/s, how high is the cliff.

Homework Equations

d= v1t + 1/2at^2
v2^2 = v1^2 + 2ad

The Attempt at a Solution

I tried using d = vt since we're given the speed of sound and the time taken for the sound to reach our ears. Since sound is unaffected by gravity, i thought i could straightaway use that formula, but I guess I was wrong. This is how far I got up to. Can someone give me a hand?

Thanks

 

[cristo]

You can use d=vt for the sound. However, note that we are told that 3.2s after the rock is dropped, we hear it hit the ocean, not that the sound takes 3.2s to reach our ears.

Use d=vt to obtain the time taken for the sound to reach out ears iafter the rock hits the ocean(in terms of d). We then know that the rock takes (3.2-t)s to fall. Can you write another equation for the rock as it falls?

 

[m2003]

for your question! Calculating the height of a cliff using the time delay of sound is a classic kinematics problem. To solve it, we can use the equations you mentioned, but we also need to take into account the distance the rock has fallen before it reaches the water.

First, let's label our variables. We know the speed of sound is 340 m/s, the time delay is 3.2 seconds, and the acceleration due to gravity is 9.8 m/s^2. We also know that the distance the rock falls is the same as the height of the cliff, which we will label as "h."

Next, we can use the equation d = v1t + 1/2at^2 to calculate the distance the sound travels. Plugging in our known values, we get:

d = (340 m/s)(3.2 s) + (1/2)(9.8 m/s^2)(3.2 s)^2
d = 1088 m + 51.2 m
d = 1139.2 m

Now, we can use the equation v2^2 = v1^2 + 2ad to find the initial velocity of the rock before it falls. We know the final velocity (v2) is 0 m/s, so we can solve for v1:

0 m/s = (340 m/s)^2 + 2(-9.8 m/s^2)h
0 m/s = 115600 m^2/s^2 - 19.6h
19.6h = 115600 m^2/s^2
h = 5903.06 m

Therefore, the height of the cliff is approximately 5903 meters. Keep in mind that this is just an estimate, as we have rounded some of our numbers. Also, it is important to note that this calculation assumes the speed of sound is constant and that there is no wind or other factors that could affect the sound's travel time. Nonetheless, this is a good approximation and a great way to practice using kinematics equations. I hope this helps!