If we numerically compute the value of a certain quantity using some potentially

Question

If we numerically compute the value of a certain quantity using some potentially complicated methods, at the end when we get a result, we can perform a rough check on our result by estimating what the result should be, and comparing this estimate to our computed result. Similarly, if someone makes an assertion to you about the numerical value of some quantity, you can perform a quick, rough check of that assertion through estimation. In other words, it's a very useful, quick, way to call someone out for claiming something ridiculous. We'll encounter some examples of this in the problems below. Even when we may not know that to systematically compute the numerical value of quantity, an estimate using some reasonable assumptions can give us a reasonable idea of its value. NO CALCULATORS ALLOWED ON THESE PROBLEMS (you will not have a calculator on exams) Usain Bolt (and in fact most world-class sprinters, both male and female), can run the sprint in roughly 10 seconds. Your friend on the UCLA track team claims that she can achieve a top speed of 40 mph when she runs the 100 m sprint. Is she likely telling the truth? Explain your reasoning. An advertising for Toyota's prototype electric family sedan that the car can sustain a straight-line acceleration equal to half the acceleration due to gravity for about 20 seconds. Does this sound reasonable? Explain your reasoning. As a bank robber sitting in the vault planning how you can maximize your wealth, do you fill your suitcase with $100 bills or with gold bars? Your suitcase is the only method of transporting the loot out of the bank. As a bank robber sitting in the vault planning how you can maximize your wealth, do you fill your suitcase with $100 bills or with gold bars? Your suitcase is the only method of transporting the loot out of the bank.

Explanation / Answer

Briefcase standard sizes:

18.5 * 13.25* 4.5 (inches)
18.5*13.25*4.5*2.543 =~18075.96CM3 or 1.8m3

Therefore $100 bills volume will be-

15.686.63*0.011=1.137708cm3
briefcase size =18075.96 cm3
case when filled with the $100 bills
18075,96 /1,137708=15.888,05 USD

Briefcase when filled with gold

Density gold: 19320KG/M3

Gold price/KG=1.272,90 USD

19320*1.8=34776KG gold fits in the case

Therefore the worth of the gold in case =34776*1.272,9= 44.266.370,40 USD

Therefore if burglar fills with gold it will be 44.266.370,40/15.888,05=2786.14 Times more than the bills

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