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Projectile Motion & Relative Motion formula sheet

Every formula in the Projectile Motion & Relative Motion chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 35 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 formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Motion in a plane

Position, velocity, acceleration
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.
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
Each axis separately, linked only by tt. Straight path if u⃗=0\vec u=0 or u⃗∥a⃗\vec u\parallel\vec a; else a parabola.
Adding velocities
3× asked, last 2025
∣v⃗1+v⃗2∣=v12+v22+2v1v2cos⁡θtan⁡α=v2sin⁡θv1+v2cos⁡θ\begin{aligned}&|\vec v_1+\vec v_2|=\sqrt{v_1^2+v_2^2+2v_1v_2\cos\theta}\\&\tan\alpha=\frac{v_2\sin\theta}{v_1+v_2\cos\theta}\end{aligned}
θ\theta between the vectors; α\alpha from v⃗1\vec v_1.

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Practise Projectile Motion & Relative Motion

32 more formulas 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×
  • Velocity perpendicular to launch
  • Time of flight11×
  • Maximum height10×
  • Height from flight time2×
  • Horizontal range11×
  • Maximum range, greatest height6×
  • Complementary angles9×
  • Angles 45∘±α45^\circ\pm\alpha
  • Range and height together4×
  • Equation of trajectory5×
  • Speed and energy at the top8×
  • Change in momentum2×
  • Radius of curvature

Projectile from a height

  • Horizontal projection8×
  • Angled projection from a height
  • Dropped from a moving vehicle6×
  • Jet from a hole in a tank

Relative velocity

  • Relative velocity5×
  • Crossing and overtaking2×
  • Two motions on one path1×
  • Two projectiles1×
  • Closest approach

River-boat and rain-man problems

  • Boat crossing a river6×
  • Shortest time2×
  • Shortest path (directly opposite)3×
  • Least drift when vb<vrv_b<v_r
  • Upstream and downstream1×
  • Rain and a moving person2×
  • Wind and aircraft1×

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Practise Projectile Motion & Relative Motion

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