Calculate Minimum Water Depth for Safe Cliff Jumping | Physics Help Needed

[Billly]

hello all, I need your help

I need an equation that will enable me to calculate the minimum depth of water necessary to jump from a cliff. I have searched the net for answers and checked out other threads to no avail. If anyone could knock up a nice and easy to use equation then it would be much appreciated. I realize there are many different variables to be factored in but with no physics background to speak of I am really going to struggle with calculating it.

I've included some of my stats for example purposes:
weight: 75kg
height 183cm
shoe size 10
water is fresh water, slow moving.

For your information I'm eyeing up a 60 foot jump from a waterfall gorge - of course, any help given will be purely hypothetical and in no way leave you at all responsible for my actions.

 

[JoAuSc]

There are difficulties with getting an analytical expression for the depth you sink (first, the differential equation is difficult to solve, and second, it's hard to find the time t when your velocity stops, which is even more difficult since that time t changes as your initial velocity changes.) Your best bet is to write a program on a computer that simulates an object falling into water which stops itself once v = 0. I tried to write a similar program a while back but I had difficulties filling in all the parameters like the buoyancy, the drag coefficient, the area, etc., especially considering that the last two parameters change depending on how you fall into the water. I suppose one way to get accurate parameters would be to do a few test jumps at safer heights and record enough data so you can make a good guess as to what the missing parameters are, though it'll be difficult measuring how far you sink into the water.

 

[rcgldr]

Another variable is taking a curved path underwater to avoid hitting the bottom. This is what high divers (jumpers as they usually land feet first, normally a double front flip with 1/2 twist to maintain a good view of the water) do if the water is not deep enough. It's something that takes experience. A 60 foot dive is high enough that hitting the water badly (not vertical enough) could cause injury.

 

[Chronos]

Try calculating your terminal velocity after free falling 60 feet at 32 feet/s^2. If you fear betting your life on your mathematical prowess - use a watermelon. If the watermelon does not survive the plunge . . . I would hesitate to confirm the experimental result. A classic example of food for thought.

 

[Labguy]

Try calculating your terminal velocity after free falling 60 feet at 32 feet/s^2. If you fear betting your life on your mathematical prowess - use a watermelon. If the watermelon does not survive the plunge . . . I would hesitate to confirm the experimental result. A classic example of food for thought.

Very good reply. The key word is certainly TERMINAL...

 

[rbj]

i occasionally jump a 13 meter cliff into Lake Champlain here in Vermont. there are higher cliffs that people jump but i don't have the testosterone for those. even if the water is infinitely deep, there are other issues to worry about. unless you hit perfectly, the kinetic energy of falling (proportional to the height) will turn into some nasty sheering forces that might tug on parts of your body more than you would be comfortable with.

if i swim the target waters and just, as best as i can do, cannot touch the bottom with hand or foot after diving (from the surface) as deeply as i can (i can usually swim down to 4 meters), then i usually consider it good for jumping in. sometimes you need a another person (who either goes up to the cliff or stays in the target waters and is someone you trust) to help you confirm that the target waters you are checking out are the same as the waters in front of you as you stand at the precipice.

 

[rbj]

oh, another problem is the gorge. locally there is a gorge with a 15 meters cliff: http://www.kayakingphotos.com/albums/huntington0705a/page/image30.html

there are nasty currents you might not know about and there is a targeting risk. for me at the lake, it's a pretty big target to hit and all i have to think about is jumping out hard enough to miss the little cliffs below me and the possibly shallower waters that are at the water edge (and staying vertical). if you jump to hard into the pool at the gorge, you might hit shallow water on the far side of the pool. not hard enough, it's the shallow water on the near side.

think of it as shooting a basketball. you need to get it to "swish" through the net without touching the rim. but you are granted no practice shots to train your muscles. the first shot counts.