Relative Velocity

v_{A} = v_{B} + v_{A / B}

Velocity of A equals velocity of B plus the velocity of A relative to B. Rearranged, vA/B = vA − vB. For two points on a rigid body, vA = vB + ω × rA/B.

$v_{A}$ (m/s): Velocity of A (same frame)
$v_{B}$ (m/s): Velocity of B
$v_{A / B}$ (m/s): Velocity of A relative to B

Step-by-step solved example

A boat heads north at 4.0 m/s relative to the water. The current is 3.0 m/s east. Speed over ground?

v_A = v_B + v_{A/B}. Close the velocity triangle.

1. Vector sum
v_boat/g = v_boat/water + v_water/g = 3 i + 4 j m/s.
$v = 3 i + 4 j$
2. Magnitude
|v| = √(9+16) = 5.00 m/s.
$∣ v ∣ = 5.00 m/s$

Answer: 5.00 m/s

10 practice questions

0/10 correct

1.If A and B have the same velocity, vA/B is

2.vA = 10 i m/s, vB = 4 i m/s. vA/B =

3.Relative velocity of A with respect to B is

4.Airspeed 200 m/s east, wind 50 m/s west. Ground speed =

5.Boat 4 m/s north in a 3 m/s east current. Ground speed =

6.vA/B equals

7.Translating frames use the same addition for acceleration:

8.Two points on a rigid body: vA = vB +

9.vB = 12 m/s, vA/B = 5 m/s opposite to vB. vA =

10.Writing relative velocities correctly requires