These are the two questions, I have provided the correct answer for both, I just need to see the work shown so I would come up with the same answer and apply the technique to other problems.
The subject matter is Newton's law of cooling.
1) When Melvin Purvis was chasing John Dillinger in 1934, he came upon a camp fire made by the notorious bank robber some time before. He spotted the smoldering fire remnants at 12:00 noon. He called in some FBI scientists who determined when the fire was put out and said that Dillinger was somewhere in the area on foot (there were no car tracks found). Using the data that the thermal cooling time constant for a typical camp fire of the wood used is Tau = 0.45 hours, and the smoldering wood had a final temperature of 207 degrees C, and that a typical fire has a maximum temperature of 1025 degrees C, how far was Dillinger from the camp? Assume that he can travel 1.75 miles per hour on foot. Give the answer in miles. The values of temperature are actual temperatures as measured by a mercury thermometer (they did not have digital ones in 1934). Assume the outdoor temperature was 25 degrees C. Show your work.
The answer is 1.34 miles.
2) Frank was the blacksmith in old Centerville back in 1921. This was before cars became popular in that neck of the woods. He was trying to teach his son the trade but it was an uphill battle all the way. One day for example, as he was showing young Sidney how to fashion a horseshoe, he spit on the ground while pulling a red hot horseshoe from the yellow coal fire and began beating it into shape, instructing his son that "...you gotta hurry and have no draft...after one minute the temperature of the metal drops to 700 degrees Celsius but if you don't have the shop doors closed the temperature would be at only 400 degrees Celsius because the time constant in the windy situation is decreased BY exactly 2.806 minutes (so said that professor fella) and the metal cools off faster and 400 degrees Celsius ain't no good to fashion a good horse shoe....". Sadly, Sidney was only interested in the new Hollywood magazines and never really wanted to become a blacksmith and since he was constantly thinking of Serina next door, he couldn't care less.
Help Sidney out and determine the time constant of the metal with the shop doors are closed. The units of the time constant should be in minutes. Show your work.
The answer is 4 minutes.