Ship a is at a. ship B is at B, 20 nautical miles south of ship A. ship B is heading due north at a speed of 10 nautical miles per hour, while ship a is heading 60 ° south by West from a at a speed of 8 nautical miles per hour. After how many hours, is the nearest distance between ship a and ship B?

Ship a is at a. ship B is at B, 20 nautical miles south of ship A. ship B is heading due north at a speed of 10 nautical miles per hour, while ship a is heading 60 ° south by West from a at a speed of 8 nautical miles per hour. After how many hours, is the nearest distance between ship a and ship B?

Suppose that after X hours, ship a and ship B arrive at two points c and D respectively, then AC = 8x, ad = ab-bd = 20-10x,  CD2 = ac2 + ad2-2ac · ad · cos 60 ° = (8x) 2 + (20 − 10x) 2 − 2 · 8x · (20 − 10x) · 12 = 244x2 − 560x + 400 = 244 (x − 7061) 2 + 480061 ∵ when CD2 gets the minimum value, CD gets the minimum value After 7061 hours, ship a and B are the closest

Ship a sails southeast from the port at the speed of 16 nautical miles per hour, while ship B sails northeast from the same port at the speed of 10 nautical miles per hour
How far is the distance between B.C. and B.C?

26 nautical miles apart, using Pythagorean theorem
The southeast and northeast directions in the title are not stated clearly, that is, the southeast and northeast directions, that is, the 45 degree angle direction, so B and C form a right triangle with the starting point. If the starting point is a, it is not difficult to calculate that AB is 10 nautical miles and AC is 24 nautical miles

One ship sails northeast from port a at the speed of 16 nautical miles / h, and the other ship sails southeast from the port at the speed of 12 nautical miles / h. after 1.5 hours, how far is the distance between the two ships?

16 × 1.5 = 24 nautical miles, the distance between the first ship and the origin
12 × 1.5 = 18 nautical miles, the distance between the second ship and the origin
24 & # 178; + 18 & # 178; = 900, √ 900 = 30 nautical miles
After 1.5 hours, the two ships were 30 nautical miles apart

As shown in the figure, there are two fishing boats, a and B, in port B. If ship a moves along 60 ° north by east at a speed of 8 nautical miles per hour, and ship B moves at a speed of 15 nautical miles per hour in a certain direction south by East, after 2 hours, ship a goes to island m, and ship B goes to island P. the distance between the two islands is 34 nautical miles. Do you know which direction ship B is sailing?

BM = 8 × 2 = 16 nautical miles, BP = 15 × 2 = 30 nautical miles, in △ BMP, BM2 + bp2 = 256 + 900 = 1156, PM2 = 1156, BM2 + bp2 = PM2, ∠ MBP = 90 °, 180 ° - 90 ° - 60 ° = 30 °, so ship B sails along the direction of 30 ° south by East