请帮帮忙我这题数学题. relative velocity

mhuihui

At 1200 noon ,a ship ,which is at a point P,sails with a constant speed 5 knots ,on a bearing 060'.At the same time ,another ship B which is at a point A,sails with a constant speed 4 knots on a  bearing 105'.If the bearing of Q from P is 320'  at the time stated,with PQ=26.4 miles,find the shortest distance between the two ships in their subsequent motion.




为什么不能用 B relative to B （如图） 找到答案？

940809136325

At 1200 noon ,a ship ,which is at a point P,sails with a constant speed 5 knots ,on a bearing 060'.A ...
mhuihui 发表于 29-9-2010 01:11 AM

   有原图吗？？？

puangenlun

let P be the origin
then the coordinates of Q:
x=26.4*cos(130)
y=26.4*sin(130)
so P(0,0), Q(26.4*cos(130),26.4*sin(130))
*** The angle of bearing starts from north and rotate clockwise
*** The angle of coordinate starts from positive x axis and rotate anti-clockwise
*** so 320' of bearing = 130' of coordinate

puangenlun

the direction of Ship A moving:
x_A=x_P+5t*cos(30)
y_A=y_P+5t*sin(30)

the direction of Ship B moving:
x_B=x_Q+4t*cos(-15)
y_B=y_Q+4t*sin(-15)

Distance between 2 ships
d=sqrt((x_A-x_B)^2+(y_A-y_B)^2)

by using the method of calculas,
we can find out the min d