2017 Problems2017年题目
2017年A题中文及解法思路
解法思路：（a)计算直线和弧上（统称曲线）需要的无人机数量，然后计算摩天轮（龙、创建自己的图像）由多少曲线组成，最后计算总的无人机数量。
(b)摩天轮（龙、创建自己的图像）是运动的，计算运动轨迹。运动方式（1）围绕摩天轮中心转动；（2）随着摩天轮中心运动。也就是平移运动加上转动。
A题
问题：无人机集群作为空中灯光表演
Intel®开发了Shooting StarTM无人机，并使用这些无人机集群进行空中灯光表演。2016年，由一台笔记本电脑和一名飞行员控制的一组500架无人机表演了一场精心编排的灯光秀
(https://www.youtube.com/watch?v=jNIAzeU8POQ).
我们的大城市每年都有一个节日，正在考虑增加一个户外空中灯光秀。市长已要求你的团队调查使用无人机创建三种可能的天空显示的想法。
第一部分-每个显示：
a） 确定所需的无人机数量，并用数学方法描述每个无人机设备的初始位置，这将导致静态图像的天空显示（类似于焰火显示）。
b） 确定每架无人机或一组无人机的飞行路径，以设置图像动画并描述动画。（请注意，您实际上不必编写程序来设置图像的动画，但您确实需要数学地描述飞行路径。）
显示1：摩天轮
展示2：龙
显示3：创建自己的图像
第二部分-确定并讨论三显示灯光秀的要求，包括但不限于无人机数量、所需发射区域、所需空中空间、安全考虑因素和空中灯光秀的持续时间。
第三部分-给市长写一份两页的备忘录，报告调查结果，并就是否进行空中灯光秀提出建议。
您的提交内容应包括：
● 一页汇总表，
● 致市长的两页备忘录，
● 您的解决方案不超过30页，最多33页，包含摘要和备忘录。
● 注意：参考列表和任何附录不计入33页的限制，应出现在完成的解决方案之后。
Problem A
Problem: Drone Clusters as Sky Light Displays
Intel® developed its Shooting StarTM drone and is using clusters of these drones for aerial light shows. In 2016, a cluster of 500 drones, controlled by a single laptop and one pilot, performed a beautifully choreographed light show
(https://www.youtube.com/watch?v=jNIAzeU8POQ).
our large city has an annual festival and is considering adding an
outdoor aerial light show. The Mayor has asked your team to investigate the
idea of using drones to create three possible sky displays.
Part I - For each display:
a) Determine the number of
drones required and mathematically describe the initial location for each drone
device that will result in the sky display (similar to a fireworks display) of
a static image.
b) Determine the flight paths of each drone or set of drones that would animate
your image and describe the animation. (Note that you do not have to actually
write a program to animate the image, but you do need to mathematically
describe the flight paths.)
Display 1: Ferris wheel
Display 2: Dragon
Display 3: Create your own image
Part II - Determine and discuss the requirements for your 3-display light
show to include, but not limited to, the number of drones, required launch
area, required air space, safety considerations, and duration of the aerial
light show.
Part III - Write
a two-page memo to the Mayor to report the results of your investigation and
make a recommendation as to whether or not to do the aerial light show.
Your submission should consist of:
● One-page Summary Sheet,
● Two-page memo to the Mayor,
● Your solution of no more than 30 pages, for a maximum of 33 pages with your
summary and memo.
● Note: Reference list and any appendices do not count toward the 33-page limit
and should appear after your completed solution.
Problem B
Problem: Ski Slope
Winter is coming! In February 2018, PyeongChang, South Korea will
host the Winter Olympics. And, in 2022, Beijing, China will be the host city.
The Winter Olympics have over fifty ski related events in the disciplines of
Alpine, Nordic, Cross-Country, Ski Jumping, Snowboarding, and Freestyle. A
group of wealthy winter sport fans are looking for a new mountain to develop
into a ski resort that could perhaps host the Winter Olympics in the future. An
agent, calling herself Ms. Mogul, represents them.
Wasatch Peaks Ranch in Peterson, Utah, USA is for sale! This almost 13,000 acre
ranch has an estimated 5,500 acres of potential ski slopes with an 11 mile
ridgeline, a 4750 foot drop among its 24 peaks, and 15 bowls. Ms. Mogul wants
your team to identify potential ski slopes and trails on the property in order
to develop it as one of the top ski resorts in North America and a potential
future Winter Olympics location.
Part I - Given
a brochure for Wasatch Peaks Ranch, a topographic map of this area, a partial
list of North American ski resorts with comparison data, and other information
available on the web, design the new Wasatch Peaks Ranch ski area to meet the
following criteria:
- Main slopes of varying lengths
- Plenty of trails
- A total of at least 160 km of slopes (main slopes and trails)
- Distribution of slopes at approximately 20% rated beginner ( green circle), 40% rated intermediate (
blue square), and 40% rated difficult (♦ black diamond).
Part II - Rank your proposed ski area against existing ski areas/resorts
in North American.
Part III - Write
a two-page memo to Ms. Mogul reporting the results of your design and the
ranking of your proposed ski area.
Your submission should consist of:
● One-page Summary Sheet,
● Two-page memo to Ms. Mogul,
● Your solution of no more than 30 pages, for a maximum of 33 pages with your
summary and memo.
● Note: Reference list and any appendices do not count toward the 33-page limit
and should appear after your completed solution.
NOTE:
Ski trail difficulty is measured by percent slope, not degree angle. A 100%
slope is a 45-degree angle. In other words, when rise/run = 1, the slope is
100%. In general, beginner slopes ( green
circle) are between 6% and 25%. Intermediate slopes ( blue square) are between 25% and 40%. Difficult slopes (♦
black diamond) are 40% and higher. However, this is just a general "rule
of thumb." Although slope gradient is the primary consideration in
assigning a trail difficulty rating, other factors come into play. A trail will
be rated by its most difficult part, even if the rest of the trail is easy. Ski
resorts often assign ratings to their own trails, rating a trail compared only
with other trails at that resort. Also considered: width of the trail, sharpest
turns, terrain roughness, and whether the resort regularly grooms the trail.
Note that you may see differing symbols and colors in your research. Table 1
shows three examples of difficulty rating symbols.
Attachments:
Wasatch Peaks Ranch Brochure
Topographic Map of Wasatch Peaks Ranch
SkiSlopeComparison.xls
References:
http://www.skiresort.info/
https://www.mirrranchgroup.com/ranches/wasatch-peaks-ranch/
https://www.mirrranchgroup.com/ranches/wasatch-peaks-ranch/#prop-maps
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