Question

A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head-on the bodies go at right angles to each other after the collision.

Answer 1

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ANSWER::

Two bodies move in a different dimension as it is not an head on collision.

Let v₁ and v₂ be the velocities of bodies vector collision.

Collision is elastic.

Now , applying law of conservation of momentum in x - direction.

mu₁ + m x 0 = mv₁ cosα + mv₂ cos β

v₁ cosα + v₂ cos β = u₁ [Equation 1]

Now , using law of conservation of momentum in y-direction

0 = mv₁ sinα - mv₂ sinβ

v₁ sin α = v₂ sinβ [Equation 2]

Now again ,

(1/2) mu₁² + 0 = (1/2) m v₁² + (1/2) m v₂²

u₁² = v₁² + v₂² [Equation 3]

Squaring Equation 1

u₁² = v₁² cos²α + v₂² cos²β + 2 v₁v₂ cos α cos β

Equating Equation 1 and Equation 3

v₁² + v₂² = v₁² cos²α + v₂² cos²β + 2 v₁v₂ cos α cos β

v₁² sin²α + v₂² sin²β = 2 v₁v₂ cos α cos β

2 v₁² sin²α = 2 x v₁ x (v₁sinα / sin β) x cos α cos β

sin α sin β = cos α cos β

cos α cos β - sin α sin β = 0

cos (α + β) = 0 = cos 90°

(α + β) = 90°

Hope it helps!

Answer 2

Answer:

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