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 127.1 km/hr prior to hitting a stack of loose hay. If the crew member can survive an acceleration of 36.0 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?

The crew member can decelerate at a maximum of 36 g. We must convert this into meters per second squared. Moreover, the terminal velocity of the crew member must be expressed in meters per second. These are:

acceleration = 36 * -9.81 = -353.2 m/s² (negative sign due to deceleration)
velocity = 127.1 km/hr = 35.3 m/s (this will be the initial velocity upon hitting the hay stack)
The final velocity of the crew member will be 0.

We use the formula:

2as = v² - u²
2 * s * -353.2 = 0² - (35.3²)
s = 1.76 meters

The haystack must be 1.76 meters high