At noon, ship A was 1600 km due west of ship B. Ship A was travelling due north at speed of 80 km/h and ship B was travelling due west at speed of 240 km/h.
Find
(a) The distance between the two ships was d km after x hours. Expresses in terms of x.
(b) When were two ships the closest to each other? Find the distance between the two ships at that time.
F.4 MATHS?
回答 (1)
2015-12-24 11:43 am
✔ 最佳答案
a)d = √((80x)² + (1600 - 240x)²)
d = √(80²x² + 80²(20 - 3x)²)
d = 80√(x² + (20 - 3x)²)
d = 80√(10x² - 120x + 400)
d = (80√10) √(x² - 12x + 40)
b)
d = (80√10) √(x² - 12x + 40)
= (80√10) √(x² - 12x + 36 + 4)
= (80√10) √((x - 6)² + 4)
d attains its minimum when x = 6, so after 6 hours two ships the closest to each other , the distance between the two ships at that time is (80√10) √4 = 160√10 = 506 km.
收錄日期: 2021-04-20 16:09:47
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