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Collision formula sheet

Every formula in the Collision chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 24 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.

Impulse and coefficient of restitution

Momentum and impulse
3× asked, last 2023
J⃗=F⃗avg Δt=Δp⃗,∑mu⃗=∑mv⃗\vec J=\vec F_{\text{avg}}\,\Delta t=\Delta\vec p,\qquad \sum m\vec u=\sum m\vec v
Momentum conserved in every collision; KE only in elastic ones. Rebound at the same speed: Δp=2mv\Delta p=2mv.
Coefficient of restitution
5× asked, last 2023
e=speed of separationspeed of approach=v2−v1u1−u2e=\frac{\text{speed of separation}}{\text{speed of approach}}=\frac{v_2-v_1}{u_1-u_2}
Along the line of impact. e=1e=1 elastic, 0<e<10<e<1 inelastic, e=0e=0 stick.
Ball on a floor
2× asked, last 2023
vn=env0,hn=e2nh,e=h1/hv_n=e^nv_0,\qquad h_n=e^{2n}h,\qquad e=\sqrt{h_1/h}
Smooth fixed floor, dropped from hh. KE lost per bounce: fraction 1−e21-e^2.
Oblique hit on a smooth wall
v′=usin⁡2α+e2cos⁡2α,tan⁡β=tan⁡αev'=u\sqrt{\sin^2\alpha+e^2\cos^2\alpha},\qquad \tan\beta=\frac{\tan\alpha}{e}
α\alpha, β\beta from the normal; only the normal part reverses, times ee. J=m(1+e)ucos⁡αJ=m(1+e)u\cos\alpha.
Bouncing until it stops
T=2hg⋅1+e1−e,S=h 1+e21−e2T=\sqrt{\frac{2h}{g}}\cdot\frac{1+e}{1-e},\qquad S=h\,\frac{1+e^2}{1-e^2}
Total time and distance; dropped from rest at hh.

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19 more formulas in 4 topics

Elastic collision in one dimension, Inelastic collisions, Bullet–block and ballistic pendulum and Oblique collisions. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Elastic collision in one dimension

  • Head-on elastic collision7×
  • Target at rest
  • Centre-of-mass trick
  • Special cases4×
  • KE transferred (target at rest)1×
  • Two blocks and a spring2×

Inelastic collisions

  • Head-on with restitution ee
  • KE lost in a collision4×
  • Perfectly inelastic (bodies stick)6×
  • Exciting a target
  • Collision during projectile motion4×

Bullet–block and ballistic pendulum

  • Ballistic pendulum3×
  • Bullet passing through or bouncing back2×
  • Embedded, then friction3×
  • Speed before impact2×
  • Hit, then a full vertical circle2×

Oblique collisions

  • Momentum in two dimensions8×
  • Equal masses, elastic, target at rest2×
  • Elastic, unequal masses2×

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