During World War 2, there were some cases where the crew fell out of burning aircraft without a parachute and survived the fall. Assume that the crew member reached a constant terminal speed of 127.6 km/hr prior to hitting a stack of loose hay. If the crew member can survive an acceleration of 35.0 g, where g is the gravitational constant, and assuming uniform acceleration, how high a stack of hay is required for the crew member to survive the fall? - I'm completely lost. Where do I begin?

Question

shane_b · Answer

This problem is interesting so I'll take a stab at it.  Someone else should check it and see if it makes sense:

First convert 127.6 km/hr to m/s.  You should get 35.44 m/s.

Next calculate the max acceleration the person can withstand (assuming downward is negative for this problem):
$$(35)(-9.8m/s^2)=-343m/s^2$$
So here's what we have so far:$$V_{final} = 0 m/s$$$$V_{initial} = -35.44 m/s$$$$a = -343 m/s^2$$
Finally, here's the kinematic equation to use:
$$V_f^2=V_i^2+2ad$$
Rearrange it to solve for d:
$$d=\frac{Vf^2-Vi^2}{2a}$$Plug in values to get the required height:$$d=\frac{(0m/s)^2-(-35.44m/s)^2}{2(-343m/s^2)}=1.831m$$

shane_b · Answer

Basically, if the height were any lower than 1.831m, you'd exceed 35g.

anonymous · Answer

Ah, now it makes sense! I was unsure as to whether I should use 127.6 km/hr as initial velocity, and it was weird trying to think about calculating a distance from the ground up instead of the opposite. I thought I needed a really complicated formula or something. Thank you so much!!