Height of a Cliff (Only time Given)

In summary, the conversation discusses a problem involving a person throwing a rock off a cliff and the time it takes for the sound of the splash to reach the person. Using equations for distance and velocity, the height of the cliff is estimated to be around 56 meters. The key to solving the problem is to set up a system of equations and consider the relationship between the two distances and times.
  • #1
PhysGoat
2
0

Homework Statement


A person throws a rock off a cliff and hears the splash below 3.4 seconds later. If we know the speed of sound is equal to 340m/s how high is the cliff to the nearest metre?


Homework Equations


I've been trying to use, r = ut + 1/2at2 and
v2 = u2 +2ar and
v= u + at


The Attempt at a Solution


I know that the height of the cliff should be around 56 m as:

r = 0 + 4.9(3.4)2

But i don't know how to factor in the time delay of the sound :(

The answer is: (Spoiler)
52 m

Thanks
 
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  • #2
PhysGoat said:
I know that the height of the cliff should be around 56 m as:

r = 0 + 4.9(3.4)2

But i don't know how to factor in the time delay of the sound :(

Welcome to PF!

Hint: it does not take 3.4 seconds for the rock to fall, it takes slightly less than that.
 
  • #3
Nice problem, i like it. You should set up a system of 2 equations. One will be the distance when the rock falls down and the other the distance when the sound comes up.
What is the relation between the two equations and what is the relation between the two times?
 

1. What is the height of a cliff and how is it measured?

The height of a cliff is the vertical distance from the base of the cliff to the top. It can be measured using a variety of methods, such as using a measuring tape or a rangefinder.

2. Can the height of a cliff be accurately estimated without any tools?

It is difficult to accurately estimate the height of a cliff without any tools. However, some people may be able to make an educated guess based on their own height or by comparing it to objects of known height.

3. What time frame is needed to determine the height of a cliff?

The time needed to determine the height of a cliff depends on the method being used. Some methods, such as using a measuring tape, can provide an immediate measurement. Others, such as using a rangefinder or calculating the height based on the angle of inclination, may require a few minutes to gather the necessary data.

4. How does the height of a cliff affect the difficulty of climbing it?

The height of a cliff can greatly affect the difficulty of climbing it. A higher cliff will require more physical exertion and potentially more technical skills, while a lower cliff may be more easily accessible.

5. Can the height of a cliff change over time?

In some cases, the height of a cliff can change over time due to natural erosion or human activities. However, these changes are usually gradual and may not be noticeable in a short period of time.

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