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Home Q & A Board Science-Related Homework Help Mathematics
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Anonymous joshephn
wrote...
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3 months ago
Need to create an equation from the below statements, thanks

To determine the distance downwind of a turbine, we need to project the location vector y) of the turbine onto the wind vector i'.

f the wind is from direction (measured clockwise from North), then the magnitude of the x and y components of the wind direction will be sin 0 and cos 0
spectively. However, the wind is from direction 9, not towards direction 0, so the (unit length) wind vector will be (— sin 0, — cos 0). The scalar projection (i.e.
agnitude) of the location vector onto the wind vector is just the dot product of these two vectors, which is (—c sin 0, —ycos 9).
mplement the following function to compute this downwind distance.
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Replies
wrote...
#1
3 months ago
Distance is = -x sin θ - y cos θ

Explanation:

Step 1: wind direction unit vector is given by

w = (-sin θ, -cos θ)

Step 2: Dot product is given by

projection = x(-sin θ)+y(-cos θ)

Step 3: downwind distance = -x sin θ - y cos θ
Answer accepted by topic starter
AnonymousAnonymous
wrote...
#2
3 months ago
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