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 θ 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 m and 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 θemb
Pass arrow: Passes all the way through the pumpkin and continues traveling away from the archer, while the
pumpkin swings to angle θpass
Bounce arrow: Bounces off the pumpkin back toward the archer, while the pumpkin swings to angle θbounce
(a) Rank the three angles θemb, θpass, θbounce from greatest to least in the spaces indicated below. Use “1” for the greatest
angle, “2” for the next greatest, and so on. If any two or all three angles are the same, use the same number for their
ranking.
(b) In a clear, coherent, paragraph‐length response that may also contain figures and/or equations, justify your ranking
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An archer tests various arrowheads by shooting arrows at a pumpkin
that is suspended from a tr...
that is suspended from a tr...
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