Adding two displacements at an angle
"Adding two displacements at an angle" is a free, interactive Class 11 Physics simulation for NEET and JEE, built on the lesson "Adding vectors analytically" in Motion in a Plane. Turn the second leg with the slider. The orange arrow R, from start to finish, is the sum. Watch its length and the curve below. Vectors add head to tail. R² = A² + B² + 2AB cos θ, with A + B at 0°, √(A² + B²) at 90° and |A − B| at 180°. 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.
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
3 answers
- What does the "Adding two displacements at an angle" simulation show?
- Turn the second leg with the slider. The orange arrow R, from start to finish, is the sum. Watch its length and the curve below.
- 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
Free, with a link back
Teaching this idea? Put the simulation on your own page or LMS with this code.