Reference Frame Physics Example 2

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

Example 2

medium
A boat travels at 5 m/s5 \text{ m/s} relative to the water, heading directly across a river that flows at 3 m/s3 \text{ m/s}. What is the boat's speed relative to the ground, and at what angle does it actually travel?

Solution

  1. 1
    The boat's velocity and river current are perpendicular. The resultant speed relative to the ground uses the Pythagorean theorem.
  2. 2
    vground=vboat2+vriver2=25+9=34≈5.83 m/sv_{\text{ground}} = \sqrt{v_{\text{boat}}^2 + v_{\text{river}}^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83 \text{ m/s}
  3. 3
    Angle downstream: θ=tan⁡−1(vrivervboat)=tan⁡−1(35)≈31°\theta = \tan^{-1}\left(\frac{v_{\text{river}}}{v_{\text{boat}}}\right) = \tan^{-1}\left(\frac{3}{5}\right) \approx 31°

Answer

v≈5.83 m/s at 31° downstreamv \approx 5.83 \text{ m/s at } 31° \text{ downstream}
The boat's motion is described differently in different reference frames. Relative to the water, it moves straight across; relative to the ground, it drifts downstream due to the current.

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 3 medium

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

Example 4 hard

A plane flies at [formula] due north relative to the air. A wind blows at [formula] from the west (t

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