Motion in a Plane
Class 11 · Motion in a Plane
Boat in a River
Boat velocity + river current — see the resultant path and drift angle.
Key Notes
01
v_resultant = v_boat + v_river (vector addition).
02
To cross river straight: point upstream at angle φ = sin⁻¹(v_river/v_boat) — only works if v_boat > v_river.
03
Min crossing time: point boat perpendicular to current (ignore drift).
04
Min drift: use angle cos⁻¹(v_river/v_boat) from perpendicular — requires v_boat > v_river.
Formulas
Resultant velocity
General case.
Angle for straight crossing
Pointing upstream at this angle gives zero drift.
Important Points
If v_river ≥ v_boat, boat cannot make a straight crossing.
Boat in a River notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.