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Projectile Motion & Relative Motion revision notes

Every idea in the Projectile Motion & Relative Motion chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 31 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Motion in a plane

Position, velocity and acceleration vectors
1× asked, last 2024
r⃗=xi^+yj^,v⃗=dr⃗dt,a⃗=dv⃗dt\vec r = x\hat i + y\hat j,\qquad \vec v=\frac{d\vec r}{dt},\qquad \vec a=\frac{d\vec v}{dt}
Differentiate each component. Average velocity =Δr⃗/Δt=\Delta\vec r/\Delta t (displacement, not path). Body moves along v⃗\vec v.
Constant acceleration in a plane
4× asked, last 2024
v⃗=u⃗+a⃗ t,r⃗=r⃗0+u⃗ t+12a⃗ t2\vec v=\vec u+\vec a\,t,\qquad \vec r=\vec r_0+\vec u\,t+\tfrac12\vec a\,t^2
Apply the 1D equations to each axis separately; time is the only link. Constant force gives a⃗=F⃗/m\vec a=\vec F/m.
  • Path is a straight line if u⃗=0\vec u=0 or u⃗∥a⃗\vec u\parallel\vec a; otherwise a parabola. A charge released from rest under gravity plus a uniform horizontal field goes straight along the net force.
  • Quick method. Get tt from the axis where data is given, then use it in the other; each axis has its own uu and aa.
Adding velocity vectors
3× asked, last 2025
∣v⃗1+v⃗2∣=v12+v22+2v1v2cos⁡θ,tan⁡α=v2sin⁡θv1+v2cos⁡θ|\vec v_1+\vec v_2|=\sqrt{v_1^2+v_2^2+2v_1v_2\cos\theta},\qquad \tan\alpha=\frac{v_2\sin\theta}{v_1+v_2\cos\theta}
θ\theta = angle between the vectors; α\alpha measured from v⃗1\vec v_1. At 90∘90^\circ: v12+v22\sqrt{v_1^2+v_2^2}.

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Practise Projectile Motion & Relative Motion

28 more concepts in 4 topics

Projectile on level ground, Projectile from a height, Relative velocity and River-boat and rain-man problems. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Projectile on level ground

  • Position during flight3×
  • Velocity during flight5×
  • Direction of motion4×
  • Time of flight11×
  • Maximum height10×
  • Height from flight time2×
  • Horizontal range11×
  • Maximum range and greatest height6×
  • Complementary angles9×
  • Range and height together4×
  • Equation of trajectory5×
  • Speed and energy at the top8×
  • Change in momentum2×
  • Radius of curvature of the path

Projectile from a height

  • Horizontal projection8×
  • Dropped from a moving vehicle6×
  • Angled projection from a height
  • Also remember1

Relative velocity

  • Relative velocity5×
  • Crossing and overtaking2×
  • Two motions on one path1×
  • Projectiles seen from moving frames1×
  • Closest approach

River-boat and rain-man problems

  • Boat crossing a river6×
  • Shortest time2×
  • Shortest path (directly opposite)3×
  • Upstream and downstream1×
  • Rain and a moving person2×
  • Wind and aircraft1×

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Practise Projectile Motion & Relative Motion

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