Speed of a Cliff Diver: Huge Cliff Jump (original) (raw)

Introduction

This is a simple mechanics problem that any physics student should be able to solve.

In this clip, a girl starts in a wooded area. She then begins to run and gets a good running jump off a cliff. Her jump is straight out, with very little or no vertical movement. We hear a splash and the camera pans down to a scene of the girl floating in the water. The camera man is located at the top of the cliff with a good view of her jump, although he misses her entrance into the water. It is unknown whether she is unconscious at the end of the clip or dead. Through research, I found that a jump just greater than hers has a high probability of death. Her entry to the water is fairly straight with her feet leading. Therefore, if the water is deep enough, she most likely survived. To view this clip, please go to Huge Cliff Jump at killsometime.com.

Analysis

If analyzed, one can determine the following for this video:

Air Time
Height of Cliff
Velocity Upon Impact

(These will all be done assuming air resistance is negligible.)

1. Air Time

To determine the time it takes the girl in the video to fall, I watched the video and paused it at the exact second her feet leave the cliff. In Quicktime, I was able to determine that this is 3.55 seconds into the video. Then I stopped the video again when she impacted with the water, at approximately 6.01 seconds into the clip.

Time = (Impact Time) − (Take Off Time)

Time = (6.01 s) − (3.55 s)

Time = 2.46 seconds

2. Height of Cliff

All we need to find the height of the cliff is the time it takes the girl to fall and a simple physics formula.

s = x0 + v0t + ½at2

s(height of cliff) = 0 + 0 + ½(9.81 m/s2)*(2.46)2

height of cliff = 29.7 m or 97.3 ft

3. Velocity Upon Impact

After watching the video, it can be seen that the girl jumps straight out, with no vertical velocity. Therefore, to determine the velocity upon impact, all we need is the time she is in the air and the acceleration due to gravity.

velocity upon impact = (a)(t)

velocity upon impact = (9.8 m/s2)(2.46 s)

velocity upon impact = 24.1 m/s or 53.9 mph

Conclusion

A fall from a great height can be very dangerous. The very rapid acceleration that occurs when one hits the ground, or in this case water, can completely destroy the inner workings of the human body. After talking to a psychologist, it is said that a fall of over seventy feet, or about seven stories high, is guaranteed death. Water, after a certain height, behaves oddly, with characteristics upon impact similar to those of concrete. Since her height was almost half again as big as is said to be fatal, it can be concluded that the girl in this video died upon impact with the water. But I don't really know for sure.

Sources of Error

One source of error was that determining her moment of impact with the water was difficult because the cameraman missed that split second. One can see her splash and a reasonable job of guessing her time can be done.

Another source of error is that air resistance was assumed to be zero, when in reality it was not zero and slowed her descent. While it would not have been much, it would have slowed her down possibly enough to save her life.

Daniel Touger -- 2005

Physics on Film