I've explained this dozens of times on this forum, indeed a number of times on this very thread! Anyone who asks this question clearly doesn't understand how ski jumps work and why there will never be a combined cat/ramp.
To get a jet fighter off the deck of a carrier, you have to get it from 0 knots to flying speed (on average around 130+ knots). An unassisted takeoff roll on the deck is a very bad idea, because unless your flight deck is over 1000ft in length (and you'd need every inch of that length) plus a lot of wind over deck (WOD) you aren't going anywhere but into the drink. And that's without any payload hangig from the wings or much fuel in the tanks. With catapult assitance (Steam or EMCAT), you can acclerate a FULLY LADEN aircraft from 0 to 130 knots in around 300ft, given the average sizes and weights of modern naval combatttant types.
The ski jump comes between the two, and it is a way of cheating really. You are still trying to do a free roling takeoff, but halfway along the roll when the aircraft is at around 80 knots (and therefore not generating sufficient lift from it's wings to fly) the aircraft is sent into the air up the 12 degree ramp on a ballistic trajectory, just like driving over a hump backed bridge in a car. Evel Knieval and his fellow stunt riders used the same technique, and their motorbikes are still to this day not known for their aerodynaimc qualities, yet they 'fly'. Unlike those bikes and indeed cars, aircraft that have left the end of the ramp are still subject to acceleration from their engine thrust and as the continue to arc upwards they increase their velocity to reach flying speed before they reach the top of the arc, at which point they are usually about 200ft in altitude and around 800ft ahead of the carrier, and simply fly away as normal. The limits in this method are mainly to do with ramp entry speed, as hitting the ramp at anything in excess of 80 knots puts excessive stress on the nosewheel oleo, and indeed if the aircraft is to be launched at highr weights it is the takeoff roll which is extended further aft on the deck so as to reach the same speed (80 knots) at the bottom of the ramp, not to enter the ramp at higher speed.
There are still limitations, the Harrier family were the first to exploit the benefits of Ramp launch because they could supplement wingborne lift after leaving the ramp with vectored thrust. Aircraft without vectored thrust eg SU-33 and Mig-29K have to rely on the high thrust to weight ratio inherent in their designs, but to maintain this ratio aircraft weight has to be kept down, limiting payload/fuel on launch. To compensate, higher powered engines would be needed, but the extra power would be disproportionate with current engine technology. Rocket assistance is dangerous to deck crews, and te rockets could only be fired safely after leaving the ramp. Not impossible, but too risky for normal ops.
Bottom line, if you can afford a catapult system for your carriers, you fit it and don't bother with the ramp. The ramp offers no benefits if your aircraft is already leaving the front of the carrier at flying speed.
With all due respect, I would disagree in principle. The stress on the undercarriage of an carrier launch aircraft is always immense regardless of if you use a CAT or a ski.
Lets run some simple numbers, lets say a 44 ton (lets say 4000 kg), F14 is propelled down the enterprise with a .. actually i can't find the launch force, but lets use your numbers; 300 feet = 100 meters, 130 knots = 67 m/s. Work = force X displacement, assuming work = K energy retained, so F X D = 1/2 X m X V^2
F = 0.5*4000*67^2/100 = 89.8 kN; around 20,000 lbf? does this sound right?
Assuming the nose gear is 1.5 meter high, that is 135 kNm or ~100,00 lbft of moment,
Assuming the nose gear is 4 inch diameter steel rod or 100 mm with a 10 mm wall, the shear stress is XX kPa; where the modulus of rigidity for steel is ~70 GPa
These are large numbers -> if I did not do something wrong, well I am a Mech, not a Material engineer; so I have no perception of how reasonable they are.
assuming a 12 deg ski vs a flat top,..... Actually, i don't want to go into a inertia calculation as all the simplifications will make it pretty moot.
What I am willing to say is that the rate of descend with the slamming of the front wheel onto the deck when the plane traps, will most likely result in a large compressive force on the front carriage assembly than a CAT can exert on a ski jump.
There are of course merit of using CAT and Ski together, you can use a smaller carrier to launch fully loaded planes that world normally require a fairly large flat top to launch. You also have the ability to launch CAP from battle damaged carrier that have so unluckily lost it's steam plant.
And frankly, the pulley system exist already, in the form of launched roller coasters. The Formula Rossa launches its cars at 150 mph in 4.9 seconds, while the Hypersonic XLC launches at 109 mph at 1.8 seconds. these roller coasters have a 90 deg vertical ramp. Of course a roller coaster is very different than an aircraft.
Note also, most of the lift an aircraft experiences is from the angle of attack, not from the lifting profile of the wing. Infact at low speeds angle of attack generate 80% of the lift while the profile itself only 20%? And the max profile lift is when the angle of attack is around 15 deg?