## Santa Clause 3

Posted by ragknot on December 11, 2012 – 10:43 pm

Slight change from the movie question.

Two flying raindeer leave the North Pole. One flies South at 20 mph, the other flies to the right at 50 mph. How many hours does it take for them to be 210 miles apart?

December 12th, 2012 at 10:19 am

With the risk of being wrong, I’ll post first…

I’m going to say the answer is between (including) 3 and 7 hours. This is assuming your given speeds and distances are radial (correct term?) since the earth is round.

No matter how you leave the North Pole, you will be flying South. If they were to fly 180 degrees (or away) from each other, it will take only 3 hours (210/(50+20)). If they fly in the same direction, it will take 7 hours (210/(50-20)).

If you mean to say that they fly 90 degrees from each other, then I’ll have to re-calculate, but it will be more near to 5 hours.

What does “to the right” mean exactly?

Are we to assume you mean they will fly at some common altitude above earth, flying around it? Or are they flying in a flat plane tangent to the north pole?

December 12th, 2012 at 12:23 pm

My guess is 3 hours, 53 minutes, and 25 seconds if flying on the surface of a perfectly spherical Earth of radius 3963.191 miles. This also assumes that ‘flying to the right’ means flying (on the surface) toward the equator at an angle of 90 degrees from the first reindeer as opposed to flying in a straight line as a tangent to the surface.

to find the surface distance between two points on a sphere…

LAT/LONG in degrees to be translated to radians.

DEGREES/180 * Pi = RADIANS

With those LAT/LONG Radians for two points find e

e = arccos[sin(LAT1)*sin(LAT2) + cos(LAT1)cos(LAT2)cos(LONG2 - LONG1)]

distance = e*r where r for earth is estimated at 3963.191 miles.

1 minute of latitude = 1.15 miles

20 mph

= 17.391 minutes of latitude per hour

= 0.289855 degrees per hour

= 0.004831 degrees per minute

= 0.000080515298 degrees per second

50 mph

= 43.478 minutes of latitude per hour

= 0.724638 degrees per hour

= 0.012077 degrees per minute

= 0.000201288245 degrees per second

We assign a Longitude to each.

Reindeer A = 0 degrees

Reindeer B = 90 degrees (right turn from A)

Both start at Latitude +90 degrees, but move toward the equator on their own Longitude.

Their latitude decreases based on their speed, detailed above.

By 3 hours, 53 minutes, 25 seconds they are 210.0046 surface miles apart.

December 12th, 2012 at 1:29 pm

If these reindeer both fly at an altitude of 36000 feet (35951.52 to be exact) and at a temperature of -51 degrees Celcius, the radius changes to 3970 miles.

This changes the minute of latitude to 1.151976 miles.

At this altitude it takes 3 hours, 53 minutes, and 49 seconds to be 210 ’surface’ miles apart.

December 12th, 2012 at 6:29 pm

Cool, I was afraid with few ToM’s entered, there might be no answers. My answer is 3.899602102 hours, or 3 hours, 53 minutes and 58.56756619 seconds. (Let’s not consider the “vertical” distance, because we don’t know that.)

Also I wondered who would realize, all directions should be south, and to the “right?”… well it should be at a right… 90 degrees angle. So the slower one would fly 77.99204203 miles and the fast one would go 194.9801051 miles. If you square and add those, then square root the total maybe you would get 210 miles.

But is this right? No. Why? Because the movie said one was flying east and one west. But that would to easy for our ToM guys. LOL, Thanks.

December 12th, 2012 at 8:35 pm

How? Well, in one hour one goes 20 miles, the other 50 miles, and the distance would be… sqrt(20^2+50^2) or 53.85164807 miles. And 210/53.85164807 = 3.899602102 hours.

December 13th, 2012 at 7:29 am

It’s interesting to me that the distance between them is reached quicker on a sphere than on a plane.

This would not continue though as there is a max distance they would reach on the sphere (at the equator) before getting closer to each other.

Another question would be at what time would the distance be the same?

December 13th, 2012 at 3:55 pm

There must be infinite “times” that they will be that distance away, assuming they stay on their path (exactly crossing the north and south poles “90 degrees” from eachother). What would be the second time they were 210 miles apart? How many times would each have circled the earth at that time?

December 13th, 2012 at 11:01 pm

That would be hard to figure.

December 14th, 2012 at 3:09 pm

Referring to cazayoux’s comment (post 6). The distance over the surface is larger than on the plane (so they make it quicker), but the straight line distance (through the Earth) is less than on the plane (then they’d take longer).

December 21st, 2012 at 7:23 am

As first deer moves with the speed of 20mph. So after 3 hrs that deer covers 60 miles. Similarly 2nd deer covers 150 miles after 3 hrs.So if we calculate the distance it is 150 + 60 = 210.

therefore the ans is 3hrs.

ANS : 3 HRS.

December 22nd, 2012 at 9:06 am

Hi abhay. That’s how long it would take if they were going directly away from each other on a plane.

December 29th, 2012 at 12:48 am

reindeer dont fly

December 29th, 2012 at 6:38 am

… so how does Father Christmas deliver the presents then?