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Quick M1 question please

There's always one question in an exercise you can't get your head around. Can anyone help please?

An aircraft is flying at a height of 4km when it suddenly loses power and begins a vertical dive. The pilot can withstand a deceleration of 5g before becoming unconscious. What is the lowest height that the pilot can pull out of the dive? (g=9.8ms^-2).
Reply 1
Avatar for jpowell
jpowell
15
You have to work out how far the aircraft can fall, before starting a 5g upwards acceleration to avoid crashing into the earth.
Reply 2
Avatar for Fermat
Fermat
8
Hmm, should that be an upward accln of 4g ??

If the pilot is free-falling, there is no g-force acting on him, but he is still travelling downwards at an accln of 1g.
If he is flying level, there is a g-force of 1g acting on him, but he has no accln either up or down.
If he is now travelling upwards with an accln of 1g, then the g-force acting on him is 2g
.
.
.
If he is now travelling upwards with an accln of 4g, then the g-force acting on him is 5g

Split the problem into two parts.
Let the pilot fall for a distance S1 under free-fall, at an acln of 1g.
Find the final velocity.
Now let the pilot accelerate upwards at 4g, with the initial velocity just found, s.t. he just reaches the ground with zero velocity. He will have travelled a distance of S2, say.
S1 + S2 = 4km.

I get 3.2 km (using the 4g -value)

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