### Home > PC3 > Chapter 7 > Lesson 7.2.5 > Problem 7-130

7-130.

A plane flying with an airspeed of 540 mph in the direction N 45º E (45º east of north) encounters a wind blowing at 47 mph in the direction S 78º E. Homework Help ✎

What are the true speed and direction of the plane?

How long will it take the plane to travel 1000 miles in the resultant direction?

If the pilot intended to fly 1000 miles in the direction N 45º E, how far from his intended destination is he given the situation in part (b)?

Solve (magnitude of vector in part (a))*t* = 1000.

intended *distance* vector: ⟨1000cos(45°), 1000sin(45°)⟩

actual *distance* vector: ⟨ (540cos(45°) + 47cos(−12°))*t*, 540sin(45°) + 47sin(−12°))*t* ⟩

Use the time you calculated in part (b).

Determine the magnitude of the difference of the vectors in steps 1 and 2.