Physics / Unit 2: Vectors and Motion in Two Dimensions
2.5 Relative Velocity
Notes
Velocity depends on the frame of reference. Add the velocities: $\vec{v}_{\text{object, ground}} = \vec{v}_{\text{object, medium}} + \vec{v}_{\text{medium, ground}}$.
- Same direction: add. Opposite directions: subtract.
- Perpendicular (boat crossing a river): use the Pythagorean theorem.
- The crossing time depends only on the velocity straight across the river.
- Example: a boat heads across at $4 \text{ m/s}$ in a $3 \text{ m/s}$ current. Ground speed $\displaystyle = \sqrt{16 + 9} = 5 \text{ m/s}$.
Practice
A plane flies at $250 \text{ km/h}$ relative to the air into a $40 \text{ km/h}$ headwind. What is its ground speed?
Headwind opposes motion: $250 - 40 = 210 \text{ km/h}$.
A boat points straight across a 60 m wide river at $3 \text{ m/s}$. The current is $2 \text{ m/s}$. How long does the crossing take?
Only the across velocity matters: $\displaystyle \frac{60}{3} = 20 \text{ s}$.
In the same crossing (20 s, current $2 \text{ m/s}$), how far downstream does the boat land?
Drift $= 2 \times 20 = 40 \text{ m}$.
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