The nine Ring Wraiths want to fly from Barad-Dur to Rivendell. Rivendell is directly north of Barad-Dur. The Dark Tower reports that the wind is coming from the west at 52 miles per hour. In order to travel in a straight line, the Ring Wraiths decide to head northwest. At what speed should they fly (omit units)?

Question

I drew it out but got lost from there, help would be nice.

Answer 1

Let the speed of the Ring Wraiths be x miles/hr. Since they're heading northwest, we can break this down into north and west components.

The north component will be the desired speed to travel directly towards Rivendell, and the west component will be to counteract the wind to keep their path straight.

By working with right triangles, observe that the north component will be x * cos(45) which simplifies to (x * √2)/2 since cos(45) = 1/√2. The west component will be x * sin(45), which is also (x * √2)/2 since sin(45) = 1/√2.

Since the wind is blowing from the west, to counteract it, the west component should equal the wind speed (52 mph). So we have:

(x * √2)/2 = 52

Now solve for x:

x * √2 = 104
x = 104 / √2
x ≈ 73.53 miles/hr

So the Ring Wraiths should fly at approximately 73.53 miles/hr.