Dolly the Cow's Dance: A Tail-spinning Mystery

[omicron]

A Cow's Dance

A cow named Dolly was enjoying the pasture & turned to face the setting sun. Then, she decided to do a little dance. The following are the steps: she turned 180degrees to her right, 90degrees to her left, then another 45degrees to her right. She repeated the steps 250 times. At the end of the dance, where was her tail pointing?

 

[ceptimus]

Answer 1: Her tail was pointing down.

Answer 2: Her tail was pointing 90 degrees to the right of the setting sun.

Depending on your position on Earth, and the time of year, the sun can set anywhere between due north, and then westwards around to due south.

 

[omicron]

Wow! I like your answer. Didn't think about the position on Earth, and the time of year. How did you get answer 2?

 

[ceptimus]

Calculus isn't needed. If you count rotation to the right as positive (this is the opposite of what mathematicians normally do, but nevermind) then Dolly's dance takes her +180 -90 +45 which is +135 degrees. Multiply this by 250 and you find she turns to the right a total of 33750 degrees. This is 93 and 3/4 complete turns (of 360 degrees). Her face will end up pointing 3/4 of a turn to the right of the sun, and so her tail will be just a a 1/4 of a turn or 90 degrees to the right.

 

[DaveC426913]

Bzzt!

Ceptimus, you forgot the very first turn. Her tail will be pointing 135 degrees to the left of the Sun.

However, *down* is the better answer.

 

[Moonbear]

Hmm...if the sun was already setting when she started her dance, by the time she was done repeating it 250 times, I think Ceptimus' answer of "pointing down" is about the only one relevant as the sun will have completed setting by then.

 

[poolwin2001]

No the sun may have risen again.So you may have to add 180 degrees to the answer

 

[DaveC426913]

You guys are prob'ly goofin' around but: there's no relevance in the Sun's position after she's begun her dance. It's only an initial condition.