Sunday, April 10, 2011

Sunday April 10, 2011

  1. On the Boxing Day (26th Dec.), stores need to come up with curious ways to give discounts to attract customer. Here is an interesting one - the store is offering a discount of  an additional 10% every hour  -  what will be the price of an item worth $100, at 9AM, 10AM, 11AM, ..., 5PM. Think of - it the discount is on the original price or the last listed price. Since you know that there are limited quantities of each of the items,  how should you approach?  If all the customers can cooperate what could be your strategy - what if they do not want to cooperate at all?
  2. In 10 seconds, the distance that a cheetah, cyclist, and an Olympian  runner can cover are respectively 300m, 160m and 110m. What is their speed? How much they would have covered in 8 seconds or 12 seconds - assuming a constant speed? Whats the best way to find out the distance for any given time duration?
  3. A right angled triangle with base 4mts, aligned to x-axis, has an area of 6m^2. What is the slope of its hypotenuse? 
  4. Whats is the slope of a Standard Staircase?  (By the way the code for staircases is 7-11, i.e. 7 inch rise for each 11inch.)  Typically the 1st floor ceiling is about 9ft,  how many steps will it require?  Whats the linear distance one needs to reach 9ft, if each step is 11inch deep. Many places steps are made in L, U or semicircular shape - any idea why one builds these shapes?
  5.  Last few questions dealt with the slope of a straight line - which is defined to be `rise' over `run'. What can one say about slope of a curve? or a surface? How will one go about computing slope of a curve?
  6. Each electron has a charge of  1.6 * 10^-19 Coulomb.  How many electrons you need to make a charge of 1 Coulomb?
  7. Current in electrical circuits means how much charge passes through a conductor in 1 second. For example, current of 1 Ampere means a charge of 1 Coulomb has gone through the conductor in 1 second - think of how many electrons have moved through - traffic jams?   If the fuse in the house has a rating of 10 A, then how much charge has gone through the fuse in 1 second? How many electrons? 
  8. My house has an electric panel and it is rated as 100 Amp. What does that mean? Lets take any household appliance - for example a computer - and lets look at its ratings? Can we figure out how many computers can we run on a 100 Amp circuit, where we have 110 Volts. What about some more heavy duty appliance like - drier or stove. For example stove are rated for 20Amps.


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