Could a big plane like a boeing 737 land on an aircraft carrier if the carrier was going at a high speed in the same direction as the plane?

No, a landing jet is traveling at least 100 mph (more than 100 knots).

There is no way any ship, let alone an aircraft carrier, can come close to that speed.

The way an aircraft carrier gets around this problem is by having special cables which catch onto a hook on the plane to pull it to a stop.

With a huge passenger jet, this is not very feasible. In order to slow the plane to a stop before it goes off the edge, you will have to stop it so suddenly that the plane would likely rip apart from it's own momentum. It would look more like a crash than a stop if successful.

Yes it can.  But the attempt will never be made.  A C130 is bigger and heavier than a 737.  It landed on a carrier not once but 21 times in a row.  The landing conditions for a 737 would be as follows:  Minimum weight.  Turn carrier full into the wind.  Go to maximum carrier speed.  Wind deck speed at 65 mph. Hit the end then kill power then engines full back then full flaps all as fast as possible Then hit full brakes.  Look it up.

The key is not the speed of the ship, but the speed of the wind relative to the ship's landing deck.

If you could have a steady (not gusty) wind of 150 knots AND a ship heading into that wind at 30 knots, you could, in theory, land a plane at 180 knots. From the ship's perpective, the plane would simply hover over the deck and float down vertically until it touches down... without moving forward.

In practice, there are so many problems with this, such as:

--have you ever been on a ship, at sea, facing a 150 knot wind? Even an aircraft carrier would suffer (because of the waves).

--Winds of that speed are not steady.

--The "landing strip" would be moving up and down, as well as left-and-right (because of the ship riding the waves)

--A boeing 737 is much larger than the usual military jet that lands on an aircraft carrier. Many things (on the ship) would tend to be obstructions (because of the width and length of the 737)

and so on.

Evidence: A 737 typically takes around 30 seconds to slow down from 220 ft/s to 0 ft/s over 6600 or so feet of runway. An aircraft carrier is around 1/6 as long, and so would have to cover 5500 ft in 30 seconds, averaging 183 ft/s = 125 mi/h ≈ 110 knots. Maximum aircraft carrier speed is around 30 knots.

Verdict: Not remotely possible.

The higher the aircraft carrier speed, the lower the kinetic energy KE the barrier arrested-recovery catcher has to face with 

Yeah it can, if the carrier could go as fast. The plane would need to be tied down before the carrier slowed down though or the airplane could slide off because it would still be going the same speed. 

Probably not.

Landing speeds for that kind of aircraft (depending on load) are around 150 knots.  And a runway of close to a mile.  No aircraft carrier could travel fast enough to make up the difference.

The way it gets around the landing needs for other aircraft is through the use of the cable arrest system.  Planes have beefed up airframes designed specifically to handle the much higher forces at landing.

I don't think it's even possible to beef up a 737 in the same way.  It would probably end up being too heavy to get of the ground.

No, the carrier couldn't go fast enough and the 737 couldn't catch the wire, the wings are also too wide.