When navigating their crafts, ship captains and airplane pilots can often be seen drawing lines on a large map?
A cruise ship is traveling in the Atlantic Ocean at a constant rate of
40 mi/h and is traveling 2 mi east for every 5 mi north. An oil tanker is
350 mi due north of the cruise ship and is traveling 1 mi east for every 1
mi south.
a. How far is each ship from the point at which their paths cross?
b. What rate of speed for the oil tanker would put it on a collision
course with the cruise ship?
looks like the same kind of question as the one I just answered,
try to follow the same method.
To solve this problem, we can use the concept of vector addition along with the given information about the ships' movements. Let's break down the problem step by step.
a. To find the distance between the ships when their paths cross, we need to determine the point where their paths intersect.
For the cruise ship:
Since it's traveling 2 mi east for every 5 mi north, we can represent its motion with a vector: (2, 5). This means that for every 5 miles the ship travels north, it moves 2 miles east.
Let's define the initial position of the cruise ship as (0, 0) since we have no information about its starting point. We can now calculate the position of the cruise ship when the paths cross:
Position of cruise ship = (0 + (2 * x), 0 + (5 * x)) = (2x, 5x)
For the oil tanker:
Since it's traveling 1 mi east for every 1 mi south, we can represent its motion with a vector: (1, -1). This means that for every 1 mile the ship travels south, it moves 1 mile east.
The position of the oil tanker is given as 350 mi due north, which can be represented as (0, -350).
Now, let's equate the positions of the cruise ship and the oil tanker to find the point where their paths intersect:
2x = 0
5x - 350 = 0
From the first equation, we get x = 0, and substituting this value into the second equation gives us 5(0) - 350 = 0, implying -350 = 0. However, this conclusion is not feasible, indicating that there is no point of intersection between the two paths. Therefore, the ships will never cross paths.
b. Since the ships' paths do not intersect, there is no possibility of a collision. Consequently, there is no specific rate of speed for the oil tanker that would put it on a collision course with the cruise ship.
In summary, the cruise ship and oil tanker will not cross paths, and no rate of speed for the oil tanker can lead to a collision with the cruise ship.