Crossing a river
"Crossing a river" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the NCERT section "Adding vectors analytically" in Motion in a Plane. A boat's velocity through the water adds to the river current; the ground path, crossing time and drift update live. NEET has asked about this idea 1 time in 10 years of papers. JEE Main asked 40 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Adding vectors analytically in Motion in a Plane. Change the values and watch what happens.
What it shows
NCERT §3.6
A boat's velocity through the water adds to the river current; the ground path, crossing time and drift update live.
Controls
4 to try
- Sliderboat speed 1–6 m/s
- Sliderriver speed 0–4 m/s
- Sliderheading −60°…+60° from straight across
- Sliderriver width 50–200 m
Try this
Choose a heading that lands the boat directly opposite its start, then one that crosses in least time, and compare times.
Common mistake
Pointing the boat straight across to land straight opposite.
In NEET
10 years of papers
Asked 1 time in 10 years of NEET.
See the past questions: Vector Algebra, Motion in a Plane (chapter)
In JEE Main
42 shifts analysed
40 questions from Motion in a Plane across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §3.6
- To add vectors, add their components: if R = A + B, then Rx = Ax + Bx, Ry = Ay + By (and Rz = Az + Bz). The same works for any number of vectors and for subtraction.
- For two vectors of magnitudes A and B with angle θ between them, R² = A² + B² + 2AB cos θ (the law of cosines).
- The direction of R from A is given by tan α = B sin θ / (A + B cos θ); the law of sines, R/sin θ = A/sin β = B/sin α, relates the sides and angles of the triangle.
- The resultant lies between |A − B| (θ = 180°) and A + B (θ = 0°); at θ = 90° it is √(A² + B²).
- 40 m and 30 m displacements at 60° to each other give R = √(1600 + 900 + 1200) ≈ 60.8 m, at about 25° to the 40 m leg.
- Worked with components, a boat heading north across a current adds its velocity through the water to the water's velocity; the ground velocity is the vector sum.
Questions
5 answers
- What does the "Crossing a river" simulation show?
- A boat's velocity through the water adds to the river current; the ground path, crossing time and drift update live.
- What mistake does the "Crossing a river" simulation fix?
- A common mistake it clears up: pointing the boat straight across to land straight opposite.
- Has NEET asked about this idea?
- Yes. NEET has asked about this idea 1 time in 10 years of papers.
- Does JEE Main ask questions from Motion in a Plane?
- Yes. JEE Main asked 40 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Adding vectors analytically" in Motion in a Plane (Class 11 Physics).
Embed this simulation
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