# A Date Idea Analyzed

I don’t do conventions very often, but I recently went to ConBust out in Northampton, MA, while visiting some friends.  While I was there, I had a guy propose something fascinating to me.  I can’t remember the guy’s name, so if he or one of his friends sees this, post your info in the comments. (Edit: it was a dude by name of Thom Howe.)

The guy Thom had an idea for a date.  He wanted to rent a cherry picker, drive it to her door, and pick her up in it.

Then, he’d drive to the beach, and get there at just the right time to watch the sun set.

Once the sun had set, he’d activate the cherry picker, they’d be lifted up above the beach …

… and they’d watch the sun set again.

Clearly, this is an excellent idea, and any girl would be lucky to see this guy Thom at her door.  But is it plausible?  How fast and how high does the cherry picker have to go?

I tried to work out the answer for him there at the table, but there was a line of people and there wasn’t time.  But when I got home, I remembered it again, and I’ve worked out the solution.

Here’s the situation:

By the time the earth has rotated through angle theta, the cherry picker will have to have climbed to height h.

After t seconds, theta in radians is:

The height of the lift above the center of the earth is:

So the height above the surface (sea level) is:

Substituting everything so far we get this expression for the height the lift needs to reach t seconds after sunset to stay even with the sun.

Now, an actual cherry picker has a maximum lift rate (I Googled some random cherry picker specs, and 0.3 m/s is a normal enough top lift rate.)  We’ll call that rate v, so the actual height of the lift will be this:

Substituting that in and solving for v, we get this:

(That’s arcsecant, not arcsecond). This equation tells us how fast the lift has to go to get from the ground to height h in time for the sunset1.

But we can also get the answer by just trying a few different heights.  We plug it in to Google Calculator2:

and find that h=6 meters gives about the right speed.  So, given a standard cherry picker, he’ll get his second sunset when they’re about six meters up, 20 seconds later.

You might notice that I’m ignoring the fact that he’s not starting at sea level — he’s a couple meters above it.  This is actually pretty significant, since the sunset line accelerates upward, and it brings down his second-sunset height quite a bit.  If he got a faster lift, or used an elevator, the correction would become less necessary.  Extra credit3 for anyone who wants to derive the expression for the height of the second sunset given the lift speed and height of first sunset. For now, I recommend he dig a hole in the sand and park the lift in it, so their eyes are about at sea level4.

1 Ideally, we’d solve for h, but it’s inside the arcsec and that looks like it’s probably hard. Do one of you wizards with Maple or Mathematica wanna find the result?

2 If you work in one of the physical sciences and don’t use Google Calculator for all your evaluatin’, you’re missing out.  I wish there were a command-line version so I could more easily look/scroll through my history.  I know Google Calculator is largely a frontend to the unix tool units, but it’s better than units and available everywhere.

3 Redeemable for regular credit, which is not redeemable for anything.

4 I suggest a day when there aren’t many waves.

## 487 thoughts on “A Date Idea Analyzed”

1. I’m not sure about the cherry picker part, but the double sunset thing does work. My grandparents have a cottage on Seneca lake in New York, and there’s a fairly big drop between the cottage and the lake. If you stand on the dock, you can watch the sunset, then run up the stairs to the cottage and watch the sun set again. (Disclaimer: you don’t actually get a repeat of the entire sunset, since there is a minute or two between when the bottom of the sun touches the horizon, and the top of the sun disappears, and you only get a repeat of the last couple seconds)

Like

2. Does it have to be at a beach? Could it be at, say, a landfill?

Like

3. Pingback: [what if]前传：陪我在海边看海……两次 – AYOU资讯

4. Pingback: 科学松鼠会 – 宝宝吃的奶粉里都添了什么？ | 常映秋的实验室（镜像2）

5. I’ve seen the Sun set five times by running up a steep hill !
So it can be done………..

Like

6. Great idea. I swear I will try this one day!!!
Another idea could be to create some kind of fun-ride or rollercoaster that you could ride just around sunset to watch the sunset twice :)

Like

7. Pingback: Skyline | Ash Chetri

8. Carbon has two stable, nonradioactive isotopes: carbon-12 (12
C), and carbon-13 (13
C), and a radioactive isotope, carbon-14 (14
The half-life of 14
C (the time it takes for half of a given amount of 14
C to decay) is about 5,730 years, so its concentration in the atmosphere might be expected to reduce over thousands of years.
1: Formation of carbon-14
2: Decay of carbon-14
3: The equation is for living organisms, and the inequality is for dead organisms, in which the 14
C then decays (See 2).
However 14
C is constantly being produced in the lower stratosphere and upper troposphere by cosmic rays, which generate neutrons that in turn create 14
C when they strike nitrogen-14 (14
N) atoms.
The carbon dating process is described by the following nuclear reaction, where n represents a neutron and p represents a proton
n + mathrm{^{14}_{7}N^+} rightarrow mathrm{^{14}_{6}C} + p

Like

9. Pingback: [what if]前传：陪我在海边看海……两次 | 创想

10. Pingback: [what if]前传：陪我在海边看海……两次 | 创想

11. Thank you very much., You are a good writer.
In addition to art that will give you good
I congratulate you

Like

12. Pingback: Skyline | Ash Chetri

13. C is constantly being produced in the lower stratosphere and upper troposphere by cosmic rays, which generate neutrons that in turn create.

Like

14. When I was placing down the place of a server for a particular web page, I exercised where within the lines it should drop. This is not really for the objective of informing you anything useful about that web page, but rather to recommend that IPs can be placed as exclusive factors on this map. executive desk

Like

15. Note: for the next few times I’ll be operating on t-shirt purchases and then I have a marriage to go to, so I may not be able to examine over your rule until next this week. Drivers

Like

16. Pingback: How High Can We Build? |

17. Then his last 100 pages are just some general calls for more research, some rather abstruse appendices that chart the passage of various religious memes through a culture, and some pretty wishful predictions of eventual rapprochement between the religious and the “bright.” Form 990n

Like

18. One way to achieve this is to find a team or an perform out affiliate who will motivate or motivate you to perform out, but what happens when you cannot find out someone to perform. go to website

Like

19. The community becomes overwhelmed with noise from various small cliques and floods of obnoxious people and the signal-to-noise ratio eventually drops to near-zero — no signal, just noise. sanibel fishing charters

Like

20. One way to achieve this is to find a team or an perform out affiliate who will motivate or motivate you to perform out, but what happens when you cannot find out someone to perform. a major brokerage

Like

21. This cord is a perfect accessory. This is also a great product because the remaining pulp is dry, not wet, which means it does extract all the juice from fruits and veggies. This is a serious book meant for those who suffer with serious disease and meant to be followed precisely. Next on my buy list are the 119 and 105 with the brass bolsters and rosewood handles for collector items. This little gem is amazing! Look no further and order it right now, you will NOT be disappointed with this purchase! We also have Perry Smith, the murderer who seems to be a decent person and claims that they never meant to kill that family. This thing just sits there in the corner turned on – using less electricity than my microwave clock. I only wish I had found it 20 years ago! One tie and the Velcro on each end just isn’t enough to keep the bumper taught and effective. These are kind of high in price compared to the aftermarket cartridges, these cost more than the cheaper knock-offs, but these print great looking photos on my Canon Pro 9000 Mark II printer.

Like

22. This little gem is amazing! Look no further and order it right now, you will NOT be disappointed with this purchase.

Like

23. Distinctly we see the difference of the colors, but where exactly does the one first blendingly enter into the other So with sanity and insanity. progressive

Like

24. Boardwalk Houses has full and improvements, such as a protected home, team home, Operate Room & Inside Gym Golf Judge, 50m Freeform Discuss Share Terrace, Going Discuss, Spread Discuss & Family Discuss Hot tub & Hydro Spa, BBQ Place Cusine. home improvement contractors

Like

25. I observed that my hypergraphia was associated with both hypomanic and depressive times but differently. When I am hypomanic I get impressive and make almost everything – poetry, publication material, blogs, academic material, abstracts, and long e-mails to friends. I also find myself arriving into realises into. more learn

Like

26. I’m not sure about the cherry picker part, but the double sunset thing does work. My grandparents have a cottage on Seneca lake in New York, and there’s a fairly big drop between the. The Best SEO Services

Like

27. Distinctly we see the difference of the colors, but where exactly does the one first blendingly enter into the other So with. address

Like

28. Its like you examine my thoughts! You appear to understand so a lot about this, like you wrote the book in it or anything.

Like

29. We are existing because we are not dead; though our daily way of life is packed with the emotional jumble of concepts, feelings, and applications, at another stage we have a low-level careful system that is always looking out for existential threats. ipad mini retina display cases

Like