View Full Version : Puzzles

10-11-2009, 15:36:44
This is from yesterday's Monday puzzle, which is a weekly feature in the NY Times Science section. I think they are interesting and confess I don't know the right answers.

Last week, we had you imagine yourself to be a perfect princess who had to choose from among the world’s most eligible princes. This week’s fictitious story, about the break-up of Tom Cruise and Nicole Kidman, is a reminder that even unions between seemingly perfect people can go horribly wrong. And both stories perfectly illustrate another recent TierneyLab topic: why we love to gossip. We enjoy the first case by vicariously living our lives through people who seemingly have it all; in the second case, we just let our bottled-up envy loose and thumb our noses at them: “You’re not so perfect, Mr. Celebrity. Nyah, nyah, nyah nyah nyah.” It’s something that we can enjoy with our baser instincts both going in and coming out.

Of course, here at the Lab, we have much more lofty motives: we want to continue to give you Aha! insights, this time into the principles of physics. So pay close attention to this story, which as mentioned earlier, is completely fictitious.

When Tom and Nicole were in love, they apparently exchanged a pair of Oscar-type statuettes of each other made of solid gold. After their break-up, these former symbols of love became symbols of pain. To ease the pain, Tom Cruise hit on a stategy of “placating density.” Sorry, that should read “placating destiny.” You have to take an object that you associate with the loved one, and submerge it in the middle of a lake. If the water level rises, it symbolizes that your mental tide has turned, and it helps you to move on.

1. So, as shown in the figure, Tom Cruise took the solid gold statue of Nicole Kidman, rowed to the middle of a lake, and tossed it overboard. Did the water level rise, fall, or stay the same when the statue sank to the bottom, relative to the level when the statue was in the boat? Why?

1. a) What’s wrong with the path of the tossed statue in the figure?

1. b) It turns out that in his haste, Tom Cruise ignored another cardinal tenet of the metaphorical remedy. It seems that to get the full mental benefits, you cannot toss the pain-associated object. You have to release it gently with your hand still in contact with it when it touches the water. Can you think of a way that Cruise could have done this so that the water level rose when he released the statue in the middle of the lake and it sank to the bottom? (Note: The lake is too large for him to stand at the shore and drop the statue in the middle.)

There were two more metaphorically significant activities that Tom had to do, in order to erase the pain of the break-up.

2. The second task is termed “overcoming meanness harmonically.” Tom had to wear Nicole’s ring and run a specified distance as fast as he could on a windy day. Then he had to dash back the other way, returning to his starting point. The condition he had to satisfy was this: his average speed on the two dashes, which both had to be done the same day, had to be higher than the fastest average speed that he could achieve if there had been no wind. “No problem,” thought Tom. He waited until he had a strong wind behind him, ran the distance and then ran right back. His fastest speed without the wind was 25 feet per second. With the wind behind him, he achieved 30 feet per second. On the way back, his speed was 20 feet per second. What was his average speed? How could he have done this right?

3. The third task is called “outsmarting frictional resistance.” Tom had to take an object associated with Nicole and toss it as high as possible into the air. Then he had to catch it as it fell down. The speed with which it was falling had to be higher than the speed at which it was thrown.

Now it is clear that if an object is thrown up at a certain speed and then it falls down under the influence of gravity, its speed when it reaches the point from which it is thrown will be exactly the same as on the way up if there were no air resistance. However, in real life, air resistance causes a frictional force that is proportional to the object’s speed at every point. On the way down, will the actual speed of the object at the starting point be the same, or higher or lower than it was on the way up? How can Tom Cruise satisfy the third task?

I don’t know whether these three tasks actually ease the psychological pain of a break-up, but all these problems have insights about physics that can help you understand fundamental ideas without complicated calculations. If you figure out the physics, you can also explain the names of these psychological tasks.

Here (hopefully) is the image referenced in the first problem:


Scabrous Birdseed
10-11-2009, 16:54:33
I've not done any physics since junior high so these are all guesses.

1. Falls slightly? Displacement of weighed-down boat volume > displacement of statue volume?

1 a. Fairly obvious, come on.

1 b. Swim out - no displacement volume change if you stay still in the water.

2. I can think of a million cheat solutions to this - using different equipment in different directions, specifically waiting for the winds to change (time between dashes wasn't specified) etc.

3. Slower? Stand on a hillside, throw it at a forward angle and run to catch it?

Cheshire Cat
10-11-2009, 17:20:31
MAPOTHER???? (http://tierneylab.blogs.nytimes.com/2009/11/09/monday-puzzle-moving-on-with-aha-moments/?em)

11-11-2009, 09:02:29
1. Lake level falls, when it's in the boat it displaces it's weight, when it's in the water it displaces it's volume. Since it's gold we know it's denser than water so will displace less water when it sinks.
1a. It's loopy
1b. As it's Tom Cruise... he could use a mission impossible style harness to abseil down to the centre of the lake from a helicopter so he's hanging upside down just above the water, then drop the statue in.
2. Ran there with the strong wind then waited for the wind to drop before running back.
3. Throw it in the air when he's moving downwards on an open air lift. So by the time he catches it, he's much lower than when he started and the thing has more time to accelerate under gravity.

11-11-2009, 09:28:03
I'm denser than water. Does that mean I displace less water when I sink?

Cheshire Cat
11-11-2009, 15:44:18
I'm denser than water. Does that mean I displace less water when I pee in the sink?

11-11-2009, 15:47:31
Drekkus: marginally denser than water.

11-11-2009, 15:59:39
The loopy pattern seemed so obvious I just assumed he was referring to something else.

As for 3, I guess you could simply throw it up from your shoulder and catch it at your feet.

As for 2, I don't think you can assume you will necessarily experience reduced wind speeds later in the day.

11-11-2009, 16:00:54
He did say that Tom specifically waited for the wind to be really strong before running, thus implying you could also wait for it not to be so strong.

11-11-2009, 16:01:44
Drekkus: marginally denser than water

Drekkus: marginally denser than water that is less dense than him.

11-11-2009, 16:19:59
I don't see how 2 is possible with a constant wind speed. Let's assume a distance of 600 feet. With no wind, it would take him 24 seconds to cover that distance. With a constant wind, it would take him 25 seconds to cover the same distance, by my calculations (300 feet at 30 ft/sec = 10 seconds + 300 feet at 20 ft/sec = 15 seconds for a total of 25 seconds).

11-11-2009, 17:04:01
But it tells us in the question the wind speed isn't constant throughout the day.

Cheshire Cat
11-11-2009, 17:12:15
He did say that Tom specifically waited for the wind to be really strong before running, thus implying you could also wait for it not to be so strong.

or he could just help his running with a sail or a kite with favorable wind, and drop or fold it on his way back

btw... "harmonically"... could it hint to a non-straight path?
start-finsih line being the same, but shorter path against the wind?

(he could... map-other paths... :nervous:)