Riddle #472

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Question: You have two coconuts and you want to find out how high they can be dropped from a 100 story building before they break. But you only have $1.40 and the elevator costs a dime each time you ride it up (it's free for rides down).

How can you drop the coconuts to guarantee you will find the lowest floor they will break at, while starting and ending at floor 1?

Note: They break when dropped from the same height and they don't weaken from getting dropped.

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By: THWeaver on 22/1/16

Ignore the elevator and instead stand outside of the building. Take a rock and approximate its volume through a rough estimation of measurement, then find a small pool, semi-cylindrical pool of water; place the rock in and measure the displacement of the water. Using the values of density and volume you just found, calculate the mass of the rock. Next, calculate the force due to gravity upon the rock through F = mg. Place the rock upon one of the coconuts. Continue to do this until the coconut is near to breaking. Once you have completed it, sum the forces of the rocks. Make certain to approximate the mass of the coconut as you did the rock.\n\nNow, understanding that F = mg + (mgh / 2d), you can solve for the correct distance (height) by estimating the height of the building and dividing by the number of floors. Go floor by floor (or infer as you note the resulting force) until you get a force close to (preferably greater than) the summed forces of the rocks on the coconut.\n\nSpeaking of which, you do need to estimate the height of the building; I almost forgot that. Find a nearby lamppost and measure both its height and the length of its shadow; immediately measure the length of the building's shadow afterwards. Using the ratio of (where B is building and L is lamppost) B shadow / B height = L shadow / L height you can approximate the height of the building. As mentioned before, divide this by the number of floors in the building to get an interval of heights to test. Note: you do have to assume that each floor of the building is nearly equal in height for the last step to work properly.\n\nHuzzah for physics!

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By: musab on 12/3/15

I think the answer is wrong because when you drop second coconut you have to ride down to get coconuts so it cost more than 1.40. I can get at most floor 47. I can go floor 22 then floor 32 with first two coconuts then floor 38 and 42 with second 2 coconuts. I cannot go beyond 47 because I already use 74 dime after first and second try and 66 dime left. After I guarantee floor 42 I ride down and get 2 coconuts and go floor 46 if first coconut does not break then I ride up to 47 and drop last one even it does not break since I need to ride down to get the coconut I cannot ride up again becaues just 19 dime left. If at floor 46 first coconut breaks then drop second one at floor 44 if it breaks than the answer is 43 otherwise 44.

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