Why Did the Projectile Hit Miley Cyrus Despite Her Fall?

[VoyagerOne]

On a test today I came across a rather ridiculous question, in which I chose the incorrect answer. The problem is, based on my understanding of kinematics I am unsure as to why I got it wrong.1. The question stated: Miley Cyrus (not kidding) suddenly falls out of a tree at the exact time that a projectile is fire upon her, the projectile hits her True or False?
2. Vy=Voy+a(t) and Vx=(Vo)cos(θ)
3. I chose False... I figured, since the projectile will be aimed at an angle anticipating her position BEFORE her sudden fall from the tree, that the projectile would pass through the area where she was before falling; furthermore, since time has passed, and Miley's acceleration is -g, then she would be lower than the projectiles trajectory. Imagine a sniper shoots at her from 1km away and it takes the projectile 1sec to reach her position. Since Miley suddenly fell, she would have moved -9.81m in the time it took the projectile to reach her former position; therefore they wouldn't collide.

Additional Info: In class the teacher said the projectile is not fired directly below her, that's all the info we got.
Teachers reasoning for the answer to be true: "Do you think I would miss Miley Cyrus."

 

[voko]

I am afraid this problem is ambiguous. What does "fired upon her" really mean?

We know that if a gun is aimed properly, it will hit a stationary target. If the target is then to move, the gun will obviously miss the target.

On the other hand, if we know in advance that the target moves while we shoot we can take that into account when we aim; that is how guns shoot at moving targets.

So, both situations are possible, but we need to know how exactly the shot was set up.

 

[nasu]

If the gun is aimed at her (or any other position), the bullet will not pass through that position because it follows a parabolic trajectory and not a straight line. The bullet has a downward displacement from the line of sight. The same displacement as the falling object (the one the gun was aimed at).
So the bullet hits the target. It's a nice experiment to do in the classroom. See this, for example.
http://www.youtube.com/watch?v=cxvsHNRXLjw

 

[haruspex]

The complete argument runs like this: assume, as nasu says, that the person firing the projectile made no allowance for gravity and simply pointed straight at Miley. If it takes time t for the projectile to cover the horizontal distance to Miley, then it will be 0.5gt² below where Miley had been (i.e. below where it would have been without gravity). In the same time, Miley has fallen 0.5gt², so the projectile hits the target.

 

[Nickie]

I understand your confusion with this question. However, there are a few key factors that need to be considered in order to arrive at the correct answer.

Firstly, we must remember that projectiles follow a parabolic path, meaning they have both horizontal and vertical components of motion. In this case, the projectile is being fired at an angle, which means it will have a horizontal velocity component as well as a vertical one.

Secondly, we must consider the concept of relative motion. In this scenario, both Miley and the projectile are moving. Miley is falling due to gravity, while the projectile is moving horizontally and vertically due to its initial velocity and the effects of gravity.

Based on these factors, it is possible for the projectile to hit Miley. While Miley is falling, the projectile is also moving towards her. The horizontal component of its motion will bring it closer to her, while the vertical component will cause it to drop slightly. Therefore, it is possible for the projectile to hit Miley at the exact time she falls out of the tree.

In addition, the information given by the teacher also supports this answer. By stating that the projectile is not fired directly below Miley, it implies that it is fired at an angle, further supporting the idea that it could hit her.

In conclusion, while your reasoning may seem logical, it is important to consider all factors and concepts of kinematics in order to arrive at the correct answer. I hope this explanation helps to clarify the question for you.