1、2016 MCMProblem AA Hot BathA person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax. Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel. Aftera whil
2、e, the bath gets noticeably cooler, so the person adds a constant trickle of hot waterfrom the faucet to reheat the bathing water. The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain.Develop a model of the temperature of the ba
3、thtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water. Use your model to determine the extent to which your strategy depen
4、dsupon the shape and volume of the tub, the shape/volume/temperature of the person in the bathtub, and the motions made by the person in the bathtub. If the person used a bubble bath additive while initially filling the bathtub to assist in cleansing, how would this affect your models results? In ad
5、dition to the required one-page summary for your MCM submission, your report mustinclude a one-page non-technical explanation for users of the bathtub that describes your strategy while explaining why it is so difficult to get an evenly maintained temperature throughout the bath water. A题 热水澡一个人用热水通
6、过一个水龙头来注满一个浴缸，然后坐在在浴缸中，清洗和放松。不幸的是，浴缸不是一个带有二次加热系统和循环喷流的温泉式浴缸，而是一个简单的水容器。过一会儿，洗澡水就会明显地变凉，所以洗澡的人需要不停地将热水从水龙头注入，以加热洗浴水。该浴缸的设计是以这样一种方式，当浴缸里的水达到容量极限，多余的水通过溢流口泄流。考虑空间和时间等因素，建立一个浴缸的水温模型，以确定最佳的策略，使浴缸里的人可以用这个模型来让整个浴缸保持或尽可能接近初始的温度，而不浪费太多的水。使用你的模型来确定你的策略对浴缸的形状和体积，浴缸里的人的形状、体积、温度，以及浴缸中的人的运动等因素的依赖程度。如果这个人一开始用了一种泡泡浴剂加入浴缸，以协助清洗，这会怎样影响你的模型的结果？除了要求的一页 MCM摘要提交之外，你的报告必须包括一页的为浴缸用户准备的非技术性的说明书来阐释你的策略，同时解释为什么洗澡水的温度得到均衡地保持是如此之难。
