Fall momentum is not saved when a world is closed and reopened, which can be exploited by survival mode players to avoid damage from a fall of any height by quitting immediately before impact.
Tested in Creative and Survival mode, additional testing by @unknown on Samsung Galaxy S4 (Android 5.0.1). Forward momentum may be removed similarly, but cannot be confirmed due to MCPE-8612.
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I can confirm this bug.
Samsung galaxy s3 neo , Android 4.4 .

Reconfirmed in 0.12.2

Re-confirmed in 0.13.0 build 5

Please respond and add the current version if you can reproduce this issue.

Confirmed in 0.15.4, please reopen.

This bug has been reported to our internal bug tracker for further testing and a fix. It is scheduled to be fixed in one of the future updates (no specific date can be provided).
When a world is quit while the player was falling, the player's momentum is not preserved. This means survival players can avoid fall damage by quitting right before impact, then reloading the world. I expected the player's momentum to be preserved so the quit/reload does not change the fall damage. The horizontal momentum also seems not to be preserved (for example sliding on ice) but it is much harder to observe since ice sliding momentum stops very quickly.
Samsung Galaxy S4 phone running Android 5.0.1.
To reproduce fall from high up looking down and open the options menu. When really close to the ground press Quit to Title. Reload and you player will fall gently to the ground. If you did this on survival, the damage taken will correspond to the distance you fell from the reload position, not from where your fall started.