I am looking at a problem where a woman has travelled down a simple waterslide and into a pool, then hurt her knee by striking the floor of the pool. I need to figure out how deep the pool needed to be for her to not hurt herself.
She is 165 cm tall, weighs 83 kg and can be assumed to have a foot to crotch length of about 75 cm. She was wearing a t-shirt and boardshorts.
The top of the slide is 5.6 m above ground, the end of the water slide is 1.4 metres above ground. The pool was an inflateable (above-ground) type and has a maximum depth of 1 metre, but at the time of the incident only had about 60 cm of water in it. Therefore she fell about 80 cm from the end of the slide to the surface of the water. I have worked out her velocity when she hit the surface of the water to be 9.89 m/s.
https://i.stack.imgur.com/IPlpm.jpg
I now need to figure out how deep the water needs to be to dissipate her velocity before her feet hit the bottom?
As part of this I'd like to know whether the maximum possible depth of 1 metre would have prevented her injury? Obviously increasing the water depth will equally reduce the amount of freefall from the end of the slide. I recognise some approximations on her cross section and angle of entry will need to be made. I'm happy for further assumptions/approximations to be made to simplify the problem, such as assuming her legs and torso are straight.
I found two similar problems answered very well, relating to how deep divers go into a pool depending on the height of the dive:
Equation to find how far into water you will sink depending on how high you jump from
Platform diving: How deep does one go into the water?
However these two scenarios assume velocity to be perpendicular to the ground, whereas my problem has a horizontal component of velocity, provided by the slide.
Any help appreciated!
