Reference Frame Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
A plane flies at 250 m/s250 \text{ m/s} due north relative to the air. A wind blows at 50 m/s50 \text{ m/s} from the west (toward the east). What is the plane's ground speed and actual direction of travel?

Solution

  1. 1
    The plane's velocity and wind are perpendicular. Ground speed: vg=2502+502=62500+2500=65000≈255 m/sv_g = \sqrt{250^2 + 50^2} = \sqrt{62500 + 2500} = \sqrt{65000} \approx 255 \text{ m/s}.
  2. 2
    Angle east of north: θ=tan⁡−1(50250)=tan⁡−1(0.2)≈11.3°\theta = \tan^{-1}\left(\frac{50}{250}\right) = \tan^{-1}(0.2) \approx 11.3°.
  3. 3
    The plane's actual path over the ground is 11.3°11.3° east of north at 255 m/s255 \text{ m/s}.

Answer

vg≈255 m/s at 11.3° east of northv_g \approx 255 \text{ m/s at } 11.3° \text{ east of north}
In the air's reference frame, the plane moves due north. In the ground frame, the wind adds an eastward component. Pilots must account for wind to reach their intended destination.

About Reference Frame

A coordinate system attached to a particular observer that is used to describe the positions and motions of objects.

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More Reference Frame Examples

Example 1 easy

Train A moves east at [formula] and Train B moves east at [formula], both relative to the ground. Wh

Example 2 medium

A boat travels at [formula] relative to the water, heading directly across a river that flows at [fo

Example 3 medium

Car A travels north at [formula] and Car B travels south at [formula], both relative to the ground.

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