How to Calculate Minimum Height for Safe Parachute Deployment

[stupif]

1. a free falling skydiver reaches a terminal velocity of 65m/s before opening his parachute.the parachute can provide a deceleration of 30m/[s[2]. a parchutist cannot hit the ground at a speed greater than 5m/s without risking injury. what is the minimum height at which the skydiver can open his parachute?


2. anyone can gives me some guidelines to do this question. because i don't understand what the question talking about. i don't know where i should start.

The Attempt at a Solution

 

[nayfie]

Basically they want you to calculate from what height your final velocity will be 5m/s, assuming an initial velocity of 65m/s and an acceleration of -30m/s.

 

[nayfie]

Here is a poorly drawn diagram that might help :)

http://img856.imageshack.us/img856/6927/diagramu.png

 

[stupif]

i used this formula [v[/2] = 2] + 2as
but my answer 70m. the answer is 104m.
then how?

 

[nayfie]

I get 70m too. Might be a mistake in the answers?

 

[I like Serena]

Hi stupif! Welcome to PF!

@Nayfie: I like your drawing!

And it's nice that the parachute gives a deceleration of 30 m/s2, but did you consider that gravity still accelerates you down with 9.81 m/s2?

 

[nayfie]

@Nayfie: I like your drawing!

I'm glad somebody liked it, it took me a lot longer than you'd think! :P

did you consider that gravity still accelerates you down with 9.81 m/s2?

I need more sleep. I think my brain has melted from exam study. :)

 

[I like Serena]

I'm glad somebody liked it, it took me a lot longer than you'd think! :P

I'm not telling how long it took me to make the drawing for Lajka!
But I enjoyed making it!

I need more sleep. I think my brain has melted from exam study. :)

Well get some sleep and report back!

 

[stupif]

so how to solve this question~i think about it day and night~haha

 

[nayfie]

Okay. I'll summarize everything we know and then you should be able to work this out.

g \approx 9.81ms^{-2}
a_{parachute} = -30ms^{-2}
v_{0} = 65ms^{-1}
v_{f} = 5ms^{-1}

The net acceleration will be a_{parachute} + g. Notice that the acceleration of gravity is in opposite direction to the acceleration of the parachute.

This leaves you with one unknown. The distance over which this acceleration needs to act to slow you down from 65ms^{-1} to 5ms^{-1}.

You have a formula to do this.

:)

 

[stupif]

thank you very much~i got it