# Restatement of the Problem

The year dates back to 776 BC and archers are competing in the Olympics for the first time EVER. It came down to two finalists: Koroibos and Pheidippides. Two arrows have just been fired and one is a perfect bullseye, but both archers fired at the exact same time! The audience is trying to figure out who the winner is. Using facts and measurements from the Ancient Olympic Judges, we can figure out who is the WINNER!

The Measurements:
The bullseye was exactly 5.7 meters above the ground
The target was 5 meters away from the wall behind it
Both finalists fired from the windows of the Colosseum**
Koroibos’ window was 9.55 meters from the ground and his arrow landed in the wall behind the target 4.7 meters above the ground
Pheidippides’ window was 11.47 meters from the ground and his arrow landed in the wall behind the target 4.2 meters above the ground
The arrow that went through the bullseye was at an angle of about 15ΒΊ. (Exact degree measurements were not possible – they didn’t have protractors yet!)

Try and match the winning arrow to its archer with the information provided. Your final step will be to determine whether you think it was Koroibos’ or Pheidippides’ arrow that hit the bullseye.

Your final write up must include:
Restatement of the Problem – Use your own words to describe the situation regarding the archers and what your goal is.
Diagram of the Situation – You must include a diagram of the situation with all relevant information labeled. Make it clear to a reader!
Solution with Explanations – You must use and explain calculations to determine which archer was more likely to have been declared the winner. All determinations will be based on sure numerical evidence. No assumptions!
Proposal to the Judges – Based on your answer you must decide which archer should be declared the winner. If you do not think that there is not enough evidence, state what other information you would need and if you had it, how exactly you would use it to determine a sure winner.
Remember, this final unit question is your chance to demonstrate the growth in understanding of any and all concepts from this unit. There are multiple ways to solve this problem. If you solve the problem one way but haven’t had the chance to demonstrate a concept (keep in mind similarity and trig), find a way to include the use of that concept somehow, even if it means including multiple ways of solving the problem or using a different way to check your answers!

Also…this assignment is no different than any other assignment. My expectation is that you try your absolute best, even if you’re unsure of what you’re doing is correct. I want to see the effort through your open and honest thoughts and ideas π
Name: _________________________________________________ Period _____
Restatement of the Problem
Use your own words to describe the situation regarding the archers and what your goal is.

Diagram of the Situation
You must include a diagram of the situation with all relevant information labeled. Make it clear to a reader!

Solution with Explanations
You must use and explain calculations to determine which archer was more likely to have been declared the winner. All determinations will be based on sure numerical evidence. No assumptions!

Proposal to the Judges
Based on your answer you must decide which archer should be declared the winner. If you do not think that there is not enough evidence, state what other information you would need and if you had it, how exactly you would use it to determine a sure winner.

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