Question

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

Answer 1

Bounce 1 , pass 3, emb2

Step-by-step explanation:

(By the way I am also doing that question on College board physics page) For the Bounce arrow, since it bumps into the object and goes back, it means now it has a negative momentum, which means a larger momentum is given to the object. P=mv, so the velocity is larger for the object, and larger velocity means a larger kinetic energy which would result in a larger change in the potential energy. Since K=0.5mv^2=U=mgh, a larger potential energy would have a larger change in height which means it has a larger angle θ with the vertical line. Comparing with the "pass arrow" and the "Embedded arrow", the embedded arrow gives the object a larger momentum, Pi=Pf (mv=(M+m)V), it gives all its original momentum to the two objects right now. (Arrow and the pumpkin), it would have a larger velocity. However for the pass arrow, it only gives partial of its original momentum and keeps some of them for the arrow to move, which means the pumpkin has less momentum, means less velocity, and less kinetic energy transferred into the potential energy, and means less change in height, less θangle. So it is Bounce1, pass3, emb2.