physics急問 - Ans.fyi 參考答案

physics急問

2012-11-07 6:53 am

小弟對以下問題完全無從入手...希望有人能夠解答

A ship B is steaming on a straight south-east at a uniform speed of 15km/hr.Another ship A,is a distance of 10km due north of B and steams at a speed of 12km/h.Find the course that A must steer in order to get as close to B as possible,and their minimum distance apart.

thx a lot

回答 (1)

天同

2012-11-07 11:45 pm

✔ 最佳答案

There is a rule, which states that in order for ship A to get as close to ship B as possible, the direction of the "relative velocity of ships B to A" must be perpendicular to the "velocity direction of ship A".

Thus, the three velocity vectors, namely the "velocity of ship A", "velocity of ship B" and "relative velocity of ship B to A", form a right-angle triangle, with the "velocity of ship B" as the hypothenus.

Let angle a be the angle between the sides of the triangle representing the "velocity of ship A" and "velocity of ship B", then

cos(a) = 12/15
i.e. a = 36.87 degrees
Thus direction at which ship A steers = (45+36.87) degrees = 81.87 degrees south of east.

For explanation of the rule, you may refer to the youtube movie given below:

http://www.youtube.com/watch?v=1f8is-tLDZc

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