Problem 2: Growing food for a lunar colony. A second division within SpaceX is responsible for developing methods to grow food either in space or on a planetlmoon colony. Among the many vegetables to grow, the division focuses on corn. However, it has not been easy for them to model how to grow space corn. The division management provides you with the basic principles: 0 The corn stalk is approximated as a solid circular column 0 The growth rate of corn (y) is composed of two parts: a basal growth rate (yb) and a stress- based growth rate (73). The stress-based growth rate (incheslday) is directly proportional to the axial stress (or) placed along the length of the stalk. Y = 1's + Yb not) = a - 000 where yb=.17 incheslday and a has units (inches!(day* Pascal)). Please remember that as the corn grows in height, there will be more stress placed on the stalk. As a result, the total growth rate (y) change over time. 0 As a first order approximation, the axial stress (o(x)) in the corn stalk follows the equation: 00) = prx - x) where L is the height of the corn stalk, p is the density, x is the height from the ground, and g is the gravitational constant. This means that the stress-based growth rate will change relative to the height from the ground. At the top of the stalk, the stress-based growth rate is zero because o(x=L)=0. The stress-based growth rate is largest at the base of the stalk (x=0) because the stress is largest at this point. The group knows that com is best harvested when it is > 6 feet in height. A survey of individual farms showed the growth of individual corn stalks over time on earth (see attached Space corn.xls le). For these data, you can assume the basal growth rate is the same across samples. a. The division would first like to know the average stressubased growth rate constant, ya, for corn on earth. They know there might be some fluctuations in the average growth rate constant for different stalks of corn and they want to account for this range. Determine this range, reporting the range as a 95% condence interval. b. In planning for a reduced gravity environment, the division head realizes that the stressbased growth rate will change (see above equations). The division head would also like to know how long does one need to let the corn grow on the moon before it is harvested? Again, be specic in your answer and account for a range of durations, reflecting the range of growth constants and any other factors that you believe are important. c. If corn is the primary calorie source for occupants of a moon colony, how much corn needs to be planted, and at what interval, to support a human in the moon colony? How much space will this require? As an example, you may learn that it is possible for one com stalk to produce 24 ears of corn, and this is enough to keep a human being nourished for a total of one week. Therefore, your estimate would be to plant one cornstalk per week to keep the single human being alive. In developing your answer, please be sure to account for a range of colony inhabitants in age, sex, and size. Cite reasonable sources of information in developing your answer, and state your condence in developing your answer. d. One way to simulate earth gravity in a moon colony is to place the seedlings along the perimeter of a rotating bioreactor which is spinning at a constant speed (to). The centripetal acceleration from this constant rotation is used to mimic earth gravity. The cornstalk grows radially inward from the perimeter of the rotating bioreactor. If you used a rotating bioreaction with a 15' diameter, how long would you use this reactor (and at what speed) for your Space corn crop