Why Does Aiming Lower in Projectile Motion Miss the Target?

[oblivinated]

Any help or simply reasons why my answer is incorrect would help greatly, thanks!

Question:

A projectile is fired from a horizontal spring-loaded gun aimed directly (along the line of sight) at a distant bull’s eye. Because of the pull of gravity during flight, the projectile misses and hits a point at a distance y beneath the bull’s eye. To hit the bull’s eye, the gun should be aimed along a line of sight above the bull’s eye, a vertical distance……

http://oblivinated.staticcling.org/files/Images/PhysicsImage.gif

a) of y, exactly.
b) slightly higher than y.
c) slightly lower than y.

My Answer:

c) slightly lower than y
At first this may seem counter intuitive, however, given the very nature at aiming lower despite having to travel farther. However, given the fact that bullets fired from a gun travel at amazing speeds, aiming slightly lower than y will produce the best results. First off, by aiming above the bull’s eye and firing, I am creating two vectors: one horizontal vector and one vertical vector. The horizontal vector will carry the bullet towards the bull’s eye, while the vertical vector should give it enough distance to drop into the bull’s eye. HOWEVER, since there is now a vertical upward vector, it will reduce the vertical downward vector (gravity), WHICH MEANS that it will not drop the full distance of y. It will land slightly above the bull’s eye. Therefore, to counter the effects of hitting slightly above, you must aim slightly lower than the distance of y. The below figure should clarify things:

My Dilemma:

The reason I am asking is because I do not agree with the answer my physics professor provided (which, by the way, was b). However, I am skeptical about arguing with him. I was just hoping to see what everyone thinks. Thanks!

 

[Chi Meson]

b is correct.

The initial upward componant of the bullet's velocity does not affect the constant downward acceleration due to gravity (one's a velocity, one's an acceleration, they don't add).

Since you must aim upward, there will be less horizontal velocity, therefore it will take more time for the bullet to get to the plane of the target. The bullet will now have more time to drop away from the straight line path along which it was aimed.

Also, keep in mind that this problem assumes ideal conditions (no effects from air resistance). The high speed of a bullet earns no special treatment.

 

[oblivinated]

Thanks, you guys are awesome ^_^.