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 128.3 km/hr prior to hitting a stack of loose hay. If the crew member can survive an acceleration of 34.0 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?

Question

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 128.3 km/hr prior to hitting a stack of loose hay. If the crew member can survive an acceleration of 34.0 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 stuck on which eqaution I need to use for this.

Answer 1

constant acceleration means

v = Vo + a t
We know Vo (convert it from km/hr to meters/second)
We know a = -34(9.8)
set v = 0, we stopped and solve for t, time spent deaccelerating in the hay
then
x = Xo + Vo t + (1/2) a t^2
here x is unkown
call Xo = 0 start of deacceleration
we know Vo and t and a from above
solve for x, distance through hay

Answer 2

To determine the height of the stack of hay required for the crew member to survive the fall, we can use the kinematic equation for uniformly accelerated motion:

v^2 = u^2 + 2as

Where:
v = final velocity (in this case, the terminal velocity of 128.3 km/hr)
u = initial velocity (which is zero due to falling from rest)
a = acceleration experienced upon impact (34.0 g)
s = distance or height traveled during the fall

Now let's convert the given values to the appropriate units. We need to convert the terminal velocity from kilometers per hour to meters per second and convert the acceleration from g (gravitational acceleration) to meters per second squared.

1 km/hr = (1/3.6) m/s (conversion factor)
1 g ≈ 9.8 m/s^2 (approximation)

Given:
v = 128.3 km/hr
a = 34.0 g

Converting v to m/s:
v = 128.3 * (1/3.6) ≈ 35.6 m/s

Converting a to m/s^2:
a = 34.0 * 9.8 ≈ 333.2 m/s^2

Now we can substitute the values into the kinematic equation and solve for the height (s):

v^2 = u^2 + 2as

(35.6)^2 = 0 + 2 * 333.2 * s

We can simplify the equation by multiplying the terms:

(35.6)^2 = 666.4 * s

Now, we can solve for s:

s = (35.6)^2 / 666.4

Calculating this expression gives us:

s ≈ 1.910 meters

Therefore, a stack of hay with a height of approximately 1.910 meters is needed for the crew member to survive the fall.