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Calculus 3 vector projection problem?
Can't figure this out for the life of me. My teacher sent out solutions, but I still don't understand it. The answer should be βπ€βππππππππβ= sqrt((β12)^2+(β35)^2)=1.58 ππ/βπ.
A 100-meter dash is run on a track in the direction of π£β=2πΜ+6πΜ. The windβs velocity is given by π€β=5.5πΜβ3.5πΜ. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr.
Can anyone explain this?
1 Answer
- EMLv 78 years agoFavorite Answer
The magnitude of the projection of w onto v could be expressed as
w βͺ (unit vector in the direction of v)
unit vector in the direction of v:
v / ||v|| =
<2, 6> / sqrt[2Β² + 6Β²] =
<2, 6> / [2sqrt(10)] =
<1, 3> / sqrt(10)
w βͺ v / ||v|| =
<5.5, -3.5> βͺ <1, 3> / sqrt(10) =
[5.5 - 3.5(3)] / sqrt(10) =
-5 / sqrt(10) β -1.58 km/h (in the opposite direction of the runner)
