2 an archer shoots three arrows which follow the...

2. An archer shoots three arrows which follow the trajectories shown. All are shot from the same position. Answer the following questions and explain your reasoning. z • Which arrow was in the air for the longest amount of time? • Which arrow had the smallest initial speed? • Which arrow initially had the largest z component of velocity? x

Pictured below are eight arrows that have been shot horizontally, i.e., straight out, by archers on platforms. All of the arrows are identical, but they have been shot at different speeds from platforms of varying height. Specific values for the speeds and of varying heights are given in the figures. All of the arrows miss the targets and hit the ground. Rank these arrows, from longest to shortest, on the basis of how long it takes the arrows to hit the ground. That is, put first the arrow that will take the longest time from being shot to hitting the ground, and put last the arrow that will take the shortest time. Scratch work: 6 m/s 7 m/s 8 m/s 15 m/s 40 m 40 m 20 m 30 m A B C D 10 m/s 12 m/s 9 m/s 5 m/s 20 m 20 m 30 m 30 m E F G H Longest 1 ___ 2 ___ 3 ___ 4 ___ 5 ___ 6 ___ 7 ___ 8 ___ Shortest Or, all of the arrows hit the ground at the same time. ___ Please carefully explain your reasoning and/or the equation you used for your answers.

Michael S.

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