Projectiles have incorrect motion when shot from a vehicle which was entered with player velocity

When entering a vehicle (either by right click or with /ride) when the player has velocity, some (but not all) projectiles shot while riding that vehicle will be sent at unexpected angles. The projectile will be increasingly inaccurate based on how fast the player was moving when they entered the vehicle.

Steps to reproduce:
1) Summon a vehicle, like a minecart or a horse with a saddle
2) Get on the vehicle with high speed, either with a speed effect such as the one below or using freefall 

/effect give @s speed 100 50 true

3) Observe how certain projectiles like arrows from bows, snowballs, or tridents now spawn with motion in the direction the player had when they got on the vehicle

Video demo:
https://youtu.be/_iN9X6nVaOk