Skip to content

Physics · Ch 3 — Motion in a Plane

Relative Velocity

3.3.4

Relative Velocity

Relative velocity between two objects moving in a plane is defined exactly as it was for rectilinear motion, but now as a genuine vector subtraction. For an object A with velocity v⃗A\vec{v}_A and an object B with velocity v⃗B\vec{v}_B (both measured in the same reference frame, e.g. relative to the ground), the relative velocity of A with respect to B is v⃗AB=v⃗A−v⃗B\vec{v}_{AB} = \vec{v}_A - \vec{v}_B, and symmetrically the relative velocity of B with respect to A is v⃗BA=v⃗B−v⃗A\vec{v}_{BA} = \vec{v}_B - \vec{v}_A. As before, v⃗AB\vec{v}_{AB} and v⃗BA\vec{v}_{BA} always have equal magnitude and exactly opposite direction, since one is simply the negative of the other. …

Misc Ex.3.6Relative velocity of an aeroplane with respect to the wind

Worked out. An aeroplane travels northward at 300 km/hr relative to the Earth, while a wind blows from east to west at 100 km/hr. The problem asks for the velocity of the aeroplane relative to the wind. The method sets up unit vectors (north along +y, east along +x), writes the aeroplane's and the wind's velocity vectors relative to Earth, and uses v_AW = v_AE - v_WE (equivalently v_AE + v_EW, since the wind's velocity relative to the plane's frame is the negative of its Earth-frame velocity) to combine the two into a single vector, then finds its magnitude via the Pythagorean formula and its direction (an angle north of ea …

Start your 14-day free trial to unlock the full solution →
← Previous · 3.3.3Equations of Motion for an Object Travelling in a Plane with Uniform AccelerationNext · 3.3.5 →Projectile Motion