Does the iPhone GPS work in an airplane cruising between 30000-40000 feet?

For most practical situations, GPS will work well enough for you to track your progress but not have great coverage (less than 2m accuracy) or accurate speed over ground readings from iOS.

From an antenna / physics perspective, you may have horrendous GPS reception since you are riding inside a mostly complete faraday cage. Even if you have your phone in a window, all the visible satellites might be in a configuration where GPS is very poor or unable to generate a usable fix.

Clearly, cruising altitude is generally one of the best places for GPS reception as long as the antenna is placed on a tip / extremity of the plane. You don't have multi path interference to speak of, no foliage, and no hills or buildings to interfere with a clear view horizon to horizon - not to mention that your altitude will let you see more than the normal "half the sky" visibility you get on the ground at best.

The phone hardware and iOS will certainly try to get you the best fix it can once you have the device out of Airplane mode. I know many pilots that report the iOS GPS in the cockpit is quite good / on par with the other consumer and even commercial navigation products.

Domestic Satellite Navigation systems usually include limitations as a security measure. The general rule is that nothing off the shelf should be able to assist in the creation of a guided missile.

To that end most, if not all, civilian GPS units will fail or work poorly if any of the following conditions are met:

• High Altitude - Once you are higher than a mountain you are no longer a normal civilian user. This limit is usually very high though (50,000ft), more commonly edge of space rather than domestic airline altitudes.
• High Speed - If you are doing more than one or two hundred miles an hour you are probably a high speed vehicle or missile. That being said the limit could be set well above the speed of sound so that civilian aircraft are unlikely to hit it.
• High Dynamics - If you are performing high speed turns you might be a missile or air-craft evading attack. It is usually not possible for commercial passenger aircraft to perform manoeuvres that trigger these limits though.

You may find that this causes an issue when using your phone on-board an aircraft. I use to build test equipment for GNSS systems and would often find GPS units behaving strangely if I started to simulate any of the above conditions.

Poor reception due to the fuselage is also a possibility. To test if this is the limiting factor, rather than the security measures, simply try using your phone's GPS within the plane while it is on the ground before take-off. If you can get a position fix before take-off but struggle once in flight it will be the security measures limiting you. I would expect most phones to not be limited by this though. If you can use it inside a bus or train without being by a window I would expect the shielding and signal levels to be similar to inside a aeroplane.

This is from a fact, on my last trip, I was trying to see how fast the airplane was travelling using Speedometer app on iPhone 5c. It didn't work.

Speedometer doesn't show location, so I tried Strava. It also didn't show speed, but it's showing that the position on map jumped occasionally.

I don't think it's GPS signal issue, I brought a Garmin bike computer one time and it recorded the flight just fine. I still have the records of a couple of flights, it's interesting to see that planes don't just take the shortest path. The only thing that didn't look right was the altitude, since it's using barometer and the cabin is pressurised.

It will work, but you must hold the phone at the window. And sometimes it takes plenty of time to fix the signal.

I can't speak to an iPhone specifically, but an iPad Air 2 works just fine as long as I'm in a window seat. I use ForeFlight, software used for navigating while flying, all the time during commercial flights when a passenger. During the climb/descent a turn might throw it off and it'll take a few seconds to reacquire the signal, and it might require holding it right to the window to reacquire position. But in cruise, once it's got a position, I can leave it on the tray table and it'll happily show position, ground speed, and GPS-computed altitude for a half hour or more without issues. The altitude is of course slightly off because when you're in cruise the plane is flying not at a fixed "feet" altitude but rather at a given flight level.