高中vector問題 (10分)

[匿名]

2011-10-19 5:12 am

A man travelling southward as 15km/h observes that the wind appears to be coming from the west. On increasing his speed to 24km/h it appear to be coming from the southwest. Find the direction and speed of the wind.

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更新1:

the direction係(9,-15) and the speed of the wind :17.493km/h 唔係要magnitude

更新2:

書的答案 the direction係(9,-15)and the speed of the wind :17.493km/h 睇完你解釋,都唔係好明條題目唔係要magnitude

更新3:

(1)點解要W - M,唔可以m-w?? (2)ai + (b + 15)j is coming from the west, so the j component is zero 點解個風o係西邊吹黎,j component is zero? (3)ai + (b + 24)j is coming from the south west, so the i and j components are equal 點解ai + (b + 24)j is coming from the south west, i and j components are equal ?

回答 (1)

用戶10012

2011-10-19 5:06 pm

✔ 最佳答案

Let the wind be W = ai + bj.
Let the man be M.
a) M = - 15j
Wind relative to the man = W - M = ai + bj - (-15j) = ai + (b + 15)j is coming from the west, so the j component is zero, so b + 15 = 0, b = - 15.
b) M = - 24j
Wind relative to man = W - M = ai + bj - (-24j) = ai + (b + 24)j is coming from the south west, so the i and j components are equal, so a = b + 24
a = - 15 + 24 = 9
So W = 9i - 15j
magnitude = sqrt (9^2 + 15^2) = sqrt (81 + 225) = sqrt 306 = 3 sqrt 34.

2011-10-20 07:27:41 補充：
1. When you press the calculator, you will find that 3 sqrt 34 = 17.492855 = 17.493 km/hr.
2. The ' length ' of a vector is its magnitude.
3. Please read wikipedia on ' relative velocity '.

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