Cosmos Computed

Here's a simple physics puzzle: suppose you're launching a model rocket. You want the rocket to go as high as possible. Is it better to design the rocket to: A. Use all of its fuel very quickly, and then use its momentum to travel high B. Use the fuel gradually over the whole duration of the flight In other words, what is the fuel consumption rate that will maximize the height of the flight path? For this problem, we can assume that the thrust is proportional to the fuel consumption rate. I'll try to post a solution to the problem in the future. New posts every month - subscribe for free !

Imagine the universe is filled with water. Instead of empty space, every inch of it contains pure water. No planets, no stars, only water. What happens? And what would happen if an air bubble formed? The answer to this question requires a basic understanding of gravity. Gravity is very important. It helps hold matter together, bends light, and distorts space-time (which, incidentally, is how it bends light). It also makes it possible to play football, and as Americans are big football fans, they would certainly agree that we couldn't live without it. Unfortunately, many Americans don't understand how gravity works. Admittedly, scientists haven't figured out a lot of things, but we do understand it well enough to make predictions and model physical events. One of the important things about gravity is that its strength is proportional to the inverse of the square of the distance. In other words, it gets weaker as you get farther away, based on the equation: F = c/d 2 where c ...

Keystone on opening day Keystone Ski Resort just opened for the ski season on Friday. I went up to the resort that same day. There was only one run open (not including the beginner area at the top of the mountain), but it was awesome nevertheless! One of the main downsides to skiing on opening day is the number of people. There must have been about 2500 people on the mountain at the same time as me (not including the people snacking in the lodge). To keep the lines moving, the lift attendants made sure that the lift was completely full, with 4 people per chair. Even so, the wait to get on the lift took a long time. At one point when I was standing in line, a thought came to mind: the line was constantly being filled with more and more people, but it never got longer because the chair lift was carrying the people away at the same rate. So what would happen if the lift attendants only put 3 people on each chair, instead of 4? This would disrupt the balance: the inflow of skiers would be ...

I'm thinking of two common English words, W1 and W2. W1 is half as long as W2, but has twice the syllables. When combined, the two words form a phrase that can be used to refer to a nonspecific stage of a meal. The letters in these two words can be rearranged to form two new common words: W3, and W4. W3 is half as long as W4, and it also has half the syllables. The two words, when combined, may be used when telling somebody to draw with a certain art medium. What are all four words? New posts every month - subscribe for free !

212° F Let's play a little game. I'll list a bunch of possible actions. Each action will have 2 variations, (a) and (b). You choose either (a) or (b), depending on which would be safer (or less painful). Each of the questions will involve an oven hot enough to bake a cake (350° F), and a pot of boiling water (assume we're at sea level). So... would you rather: 1.     (a) Stick your hand in the oven     (b) Stick your hand in the boiling water   ... for a period of 10 seconds 2.     (a) Leave a fork in the oven     (b) Leave a fork in boiling water   ... for a period of 15 minutes. Then hold the fork tight with your bare hand. 3. Fill a jar to the top with cool tap water. Then:    (a) Place the jar in the oven    (b) Place the jar in the boiling water   ... for a specific, but unknown, period of time. Then remove the jar and put your hand in it. First see if you can figure these out yourself. They shouldn't be too...

When I was young, I would fold a sheet of letter paper in half, for origami projects. It occurred to me that the two halves looked almost the same as the whole sheet of paper - except they were smaller. I could see they weren't exactly the same shape; they were off by a little bit. But the idea stuck in my head. You can use a pen, instead of scissors, to halve the paper. Those rectangles all have the same shape, but are different sizes. One night when I was 12, I thought about my idea. I wondered if it was possible to have a sheet of paper that could be cut in half, resulting in 2 smaller versions of the same paper. That would be neat, to be able to cut a paper in half and get 2 papers that had the same exact shape. If that were possible, then you could cut  those  papers, too; and the resulting papers would have the same shape as all the other papers. You could keep cutting in half forever, and each paper, no matter how small, would have the same shape as all the ot...

Here are some pictures I took. See if you can guess some things about the photos: Approximately what time of day the photo was taken at, or if it's computer-generated Which parts of the photo were computer-generated, if any The season (for outdoor photos) To view the images better, click on one. I'll give answers later. House Crayons Calendar Blue Moon Weeds and Grass

A couple of pieces of good news: First, in this post will be the answer to the problem I gave called Flipping Quarters ; and second, I'll even work through the solution! We have to figure out the average amount of money that the man pays you, minus $5. To start out, let's forget about the money and look at the actual coin flipping. Since it's about as likely for the coin to give tails as it is to give heads, you would get heads 50% of the time. So on your 1st flip, there's a 50% chance you'll get heads - a 50% chance that you'll have to stop. What is the chance that you'll have to stop immediately after the 2nd flip? There's a 50% chance that you will actually get to the 2nd flip, and a 50% chance that you'll flip heads on it. Multiply those numbers, and you get 25%. Look at the diagram to the right if you don't understand. Now for the 3rd flip: there's a 25% chance there will be one (because you got tails on the 2nd flip), and a 50% chance y...

Here's an interesting puzzle involving chance: A man in a park asks you to play a game with him. It's a form of gambling. To play, you must pay the man $5, then flip a coin repeatedly until you get heads. As soon as you get heads, you stop flipping. If you only flipped the quarter once, he'll give you $1. If you flipped it twice, you get $2. Three times, $4. Four times, $8. Each extra flip gets you twice as much money, so the longer it takes before you get tails, the more money you get. Should you play, if you have a lot of time and the man will play as many games as you want? How much money, on average, would you gain (subtracting the $5 fee)? I will give the solution in a later post .