Question of Physics

Question

Two particles of masses m₁ and m₂ move with initial velocities v₁ and v₂ along y and x axes, respectively. The particles collide at the origin and stick together and then they move with some velocity. Find the angle θ which the system of two particles makes with the horizontal in terms of m₁, m₂, v₁,and v₂.

Answer 1

Let v be the velocity of the pair after the collision.

By conservation of momentum, the vector sum of the two momenta, m₁v₁ and m₂v₂,

is the vector (m₁+m₂)v.

The projection of (m₁+m₂)v on the y-axis must equal the original m₁v₁, and

the projection of the (m₁+m₂)v on the x-axis must equal the original m₂v₂.

From those two equations we can calculate θ.

(m₁+m₂)v sin(θ) = m₁v₁

(m₁+m₂)v cos(θ) = m₂v₂

Divide the first equation by the second:

tan(θ) = (m₁v₁)/(m₂v₂)

θ = arctan((m₁v₁)/(m₂v₂))