An archer tests various arrowheads by shooting arrows at a pumpkin that is suspended from a tree branch by a rope, as shown to t

Question

1 month ago

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An archer tests various arrowheads by shooting arrows at a pumpkin that is suspended from a tree branch by a rope, as shown to t

he right. When struck head on by the arrow, the pumpkin
swings upward on the rope. The maximum angle that the rope makes with the vertical is different for each arrowhead that the archer tests. Each arrow, including its arrowhead, has the same
mass mand is shot with the same velocity vo toward the right
The arrowheads are made of different materials, however, and each behaves differently when it strikes the pumpkin, as described below.
- Embedded arrow Strikes the pumpkin and remains embedded, while the pumpkin swings to angle &emb
• Pass arrow Passes all the way through the pumpkin and continues traveling away from the archer, while the pumpkin swings to angle bass
- Bounce arrow. Bounces off the pumpkin back toward the archer, while the pumpkin swings to angle bounce
a Rank the three angles Gemb Bass and bounce from greatest to least in the spaces indicated below. Use"
three angles are the same, use the same number for their ranking
for the greatest angle, "2" for the next greatest and so on. If any two or all
_Gemb—_Bass_Bounce
b. In a clear, coherent, paragraph-length response that may also contain figures and/or equations, justify your ranking

Physics

1 answer:

Maru [3.3K] · Answer 1 · 2026-02-16T06:21:34+03:00

Answer:

Bounce 1, pass 3, embedded 2

Explanation:

(By the way, I'm also tackling that problem on the College Board physics page.) The Bounce arrow indicates a collision with the object and a reversal, reflecting it now possesses negative momentum, thus imparting greater momentum to the object. From P=mv, this implies a higher velocity for the object and a corresponding increase in kinetic energy, leading to a greater change in potential energy. Given that K=0.5mv²=U=mgh, an increase in potential energy corresponds to a larger height change, which translates to a larger angle θ with respect to the vertical. In contrast, the embedded arrow transfers all its momentum to the two objects instantly (the arrow and the pumpkin), resulting in a higher velocity. The pass arrow, however, only transfers a portion of its momentum while retaining some for its own movement, leading to diminished momentum for the pumpkin, and consequently lower velocity and kinetic energy transferred to potential energy, resulting in less height change and a smaller θ angle. Hence, the ranking is Bounce 1, Pass 3, Embedded 2.