Question

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 51o W at 14 miles per hour, and the other travels at a bearing of S 56o W at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places. ...?

Answer 1

We find the components of each liner's speed in the North direction and the West direction.
First liner:
North component = 14sin(51)
= 10.9 mph
Northward distance covered:
10.9 x 2
= 21.8 miles
West component = 14cos(51)
= 8.8 mph
Westward distance covered:
17.6 miles

Second liner:
North component = -17sin(56)
= -14.1 mph
Northward distance (negative sign because direction opposite to North):
-14.1 x 2
= -28.2 miles
West component = 17cos(56)
= 9.5 mph
Westward distance:
9.5 x 2
= 19 miles
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √(-28.2 - 21.8)² + (19 - 17.6)²
= 50 miles