1.at noon , a ship A is 60km due north of a shipB . A is sailing due east 20 km/h while B is sailing at 15 km/h due north.
(a)express the distance s km between A and B at time t.pm in terms of t.
(b)find the time and the distance between A and B when they are closest.
F.5 a.math.differentiation
2007-08-18 12:55 am
回答 (2)
2007-08-18 1:40 am
✔ 最佳答案
(a) s^2=(20t)^2+(60-15t)^2=625t^2-1800t+3600
s=√(625t^2-1800t+3600)
(b) ds/dt=d/dt(√(625t^2-1800t+3600))
=(1/2)(625t^2-1800t+3600)^(-1/2)(1250t-1800)
=(625t-900)(625t^2-1800t+3600)^(-1/2)
when ds/dt=0
625t-900=0
t=1.44
s=48
so the distance is 48km and time is 1:44p.m. when they are the closest.
參考: me
2007-08-18 1:49 am
a) S = [(60-15t)^2 + (20t)^2]^(1/2)
S= (625t^2-1800t+3600)^(1/2)
b) dS/dt = (1/2)(1250t-1800)(625t^2-1800t+3600)^(-1/2) = 0
(1/2) (1250t-1800) = 0
t = 1.44
S = [625(1.44)^2-1800(1.44)+3600]^(1/2)
= 48
2007-08-17 17:53:37 補充：
hence, ship A & B is closest when t=1.44 (1:26:24) & their distance is 48km.
S= (625t^2-1800t+3600)^(1/2)
b) dS/dt = (1/2)(1250t-1800)(625t^2-1800t+3600)^(-1/2) = 0
(1/2) (1250t-1800) = 0
t = 1.44
S = [625(1.44)^2-1800(1.44)+3600]^(1/2)
= 48
2007-08-17 17:53:37 補充：
hence, ship A & B is closest when t=1.44 (1:26:24) & their distance is 48km.
收錄日期: 2021-04-22 00:15:17
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https://hk.answers.yahoo.com/question/index?qid=20070817000051KK03354