What a cool idea! Given the moderate financial success of "extreme rides" such as bungee jumping, you just might be able to actually do this, and maybe even show enough money-making potential to get VCs to pay.
Getting down to numbers.
For starters, 10 km is way too ambitious a target altitude - only record-attempters and unfortunate military pilots ever jump from this height. Recreational skydivers usually jump from 1500 to 4500 m (the last gives a good 60+ second of safe freefall).
So what can a 100 meter long super-human-cannon/railgun achieve?
Most of the sources I checked say that a healthy person can withstand about 9 gs for up to 2 sec. Some put the number for a specially trained person as high as 15gs.
Calculating for both (and subtracting a g of actual acceleration due to the force of gravity, we have (all in units of meters and seconds):
a1= 76 136
t1=(2*d1/a1)^.5
v1=t1*a1=
(2*d1*a1)^.5= 123 165
pretty respectible "muzzle velocities".
Without air resistance, this gives max altitudes of
872 1489
pretty close to recreational skydiving altitudes.
Unfortunately, air resistance has a major effect on person-size/mass projectiles. Taking 135 m/s as the fastest freefall speed achieved by a human (higher speeds have been claimed, but not demonstrated in front of reliable witnesses), and calculating a combined drag coefficient (cf) from that, then using numeric methods in the form of this bit of M code
Code:
s m=100,cf=.055,d=100,v=123,t=0,dt=.01
f s a=v**2*cf/m+9.8,d=v*dt/2+d,v=-a*dt+v,d=v*dt/2+d,t=t+dt i v<0 w t,?10,d,?40,v,! q
s cf=.325,t=0,d0=700
f s a=v**2*-cf/m+9.8,d=v*dt/2+d,v=-a*dt+v,d=v*dt/2+d,t=t+dt i d<d0 w t,?10,d,?40,v,! q:d0=0 s d0=$s(d0=700:200,1:0)
gives the following (prettied up by hand):
Description__Mass___Drag__Vel___Alt__Time:_Up__700 __200___0
Vacuum_____________0______123___872________13____6 ___12__13
__________________________165__1489________17___13 ___16__17
Spread_____________0.325__123___375_________6_____ ____7__11
__________________________165___454_________7_____ ____8__12
Diving________100__0.055__123___659________10_____ ___12__16
__________________________165___943________12____8 ___17__21
Light_faring__100__0.02___123___772________11____4 ___14__18
__________________________165__1204________14___13 ___22__26
Heavy_faring__250_________123___828________12____5 ___15__19
__________________________165__1354________16___16 ___25__29
Vehicle______2000_________135___866________12____6 ___16__20
__________________________165__1470________17___18 ___27__31
Units are kilograms, meters, and seconds.
”Spread” means the skydiver is launched in the “spread eagle” position usually used while freefalling.
“Diving” means he’s launched in the aerodynamic dive position skydivers used to descend quickly
The various “farings” mean the skydiver is enclosed in an aerodynamic shell.
“Vehicle” means the skydiver is enclosed in a thin, rocket-shaped vehicle weighting about as much as a small truck.
Skydiving organizations insist on a minimum opening height of 700-1000 m, but with the right equipment, a 200 m opening height would probably be safe, so freefall times to those heights, as well as a “splat” height of 0, are shown.
So it looks to me as if the system alxian describes could be built to achieve a freefall experience substantially shorter than jumping from an airplane, but still enjoyable, without injuring the skydiver/human cannonball. Not only that, they’d enjoy the never-before-done experience of “skydiving up”.
don't call me skinny! i'm just ... 
<<< ... aerodynamic!
, 304 gees ?!?!?! 
, thanks uncle AL, however those numbers seem slightly excessive.. and a human occupant very likely to become soup in the attempt 
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. Just look at my threads on Perpetual Motion 
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Kinetic Launch Skydiving - coming soon to an amusment park near you?
