HAAAAAAAAAHAHAHAHA
A car door won't stop a bullet unless it's been armoured. I have shot cars before, with handguns, and the bullet will go straight through the door and then go out the other door most of the time. A door would slow down an arrow, but a good arrow fired from a powerful bow will still kill you through one. If it didn't outright kill you, you'd be very likely to crash. Arrows hurt far more than bullets.
Lemme guess, a post 2000 Asian car? Try shooting through a good old Model T door, which would be closer to steel armour (but still weaker than it). Cars have decreased in sturdiness by orders of magnitude to save on weight and cost. Hell, you could probably *punch* through a modern car door with a bit of training.
As far as accuracy goes, the *minimum* range for archery targets in old England was 220 yards. 2 and a fifth football fields. That's an appreciable distance. 300 yards was not unheard of. An exceptionally powerful crossbow could fire even farther in good hands.
Sure, you can shoot that far. But you won't hit a damn thing at that range. Hitting things with iron sights using a rifle with a barrel on the shorter end of the scale is very unreliable, with bow or crossbow it's just blind luck.
Anyway, you're severely underestimating the strength of steel armour. It was commonly proofed by firing a pistol at it, and the armour maker would encircle the dent from the bullet to draw attention to the fact that it didn't break through. Musket rounds were a different story, though. But yeah, I don't think an arrow would even come close to the force of a pistol round.