Person falls on mattress: draw speed-time graph

[alingy1]

Homework Statement

A person falls on a mattress from 4 meters. The mattress does not make him bounce. Draw the speed-time graph.

Homework Equations

Speed-time graph principles.

The Attempt at a Solution

I know the first part is a linear function, where the speed increases, because of gravity. However, the moment when the person touches the mattress and thereafter, I'm not sure what happens. We have learned Hooke's law. Should it be a curved line like the left branch of a x^2 function? I think when the person touches the mattress, the mattress increases the deceleration of the person because of Hooke's law? What do you think?

 

[Simon Bridge]

1. is the distance fallen through the air short enough to ignore air resistance?
2. is the mattress inner-sprung? How does it matter?
3. what does it mean, for the mattress, that the person does not bounce

What level is this at?
It could be that you are over-thinking the graph and you only need to show an appropriately curved line ... i.e. what happens to the acceleration after hitting the mattress?

 

[Chestermiller]

I think what the problem is looking for you to show is that the speed continues to increase even after initial contact with the mattress until the force provided by the mattress is equal to the weight of the object. In other word, there is no discontinuity in the velocity.

 

[coconut62]

Will the person die? (this is serious physics question)

Something about impulsive force ._.

 

[mlicen]

Perhaps "the person does not bounce" means that he or she does not loose contact with the mattress, meaning that after touching the mattress, you can say that the motion is the same as if the person were on a spring. In that case you have the first part where the speed is increasing linearly and the second part where it oscilates.

 

[Simon Bridge]

@mlicen: so your interpretation would be that the person+mattress can be treated as a mass+spring system?
Doesn;t that mean that, after impact, the person would execute simple harmonic motion? (i.e. not come to rest?)

However - it is more important for me to see what @alingy1 thinks about this - unless you are doing the same problem in the same course?

@coconut62: from a 4m fall - unlikely. Even without the mattress, you'd have to land funny.
The area under the force-time graph is the specific impulse - but what you need to avoid injury is to spread the curve out in time as much as you can. For a short fall, with no funny twists in the fall, no hitting your head (or other spots) on something hard, then you want to make sure that your internal organs don't get damaged in the deceleration. This is all stuff stunt-coordinators need to know about.

For a simple collision, the force-time graph is an inverted parabola - which should nicely tell OP what they need to draw the v-t graph. There are a lot of subtleties that could go into this graph though, so context is quite important.