Assumptions:
mass of Cap is ~100 kg = 220 lbs @ 1g
Vertical speed at t = 0 s is 110 m/s ~= 250 mph

I found an excellent .pdf on the military math modeling of parachuting. I'm trusting it for this post.

The pdf gives an equation for the "severity index" of brain trauma due to deformations during the deceleration.
I = [2v/(g*dt)]^2.5 * dt

It says we need to keep the index below 400 to avoid loss of consciousness or mild concussion.
Uh oh. Plugging in 110 m/s and g = 9.81 m/s^2, we need ~3.3 s to decelerate. I was hoping for something in the 1/4 of a second range.

Solve for average deceleration over that time:
v_f = v_i + a*dt
0 m/s = 110 m/s + a(3.3 s)
a = (-110 m/s)/(3.3 s) = -33 m/s^2

Solve for distance covered during deceleration:
x_f = x_i + v_i*dt + (1/2) a*dt^2
x_f = (0 m) + (110 m/s)*(3.3 s) + (1/2) (-33 m/s^2)*(3.3 s)^2
x_f = 181.5 m

***
We're in some room for making some changes. Either he needs to be 182 m tall, or a super brain that can not deform under extreme accelerations.

Which do you prefer?