Question

Repeat the preceding problem for the case when the initial speed of the second object is nonzero.

Reference Problem:
Derive the equations giving the final speeds for two objects that collide elastically, with the mass of the objects being m₁ and m₂ and the initial speeds being v₁,ᵢ and v₂,ᵢ=0 (i.e., second object is initially stationary).

a) v₁, = (m₁-m₂)/(m₁+m₂) . v₁, ᵢ + 2m₂/(m₁+m₂) . v₂, ᵢ
b) v₁, = 2m₂/(m₁+m₂) . v₁, ᵢ + (m₁ - m₂)/(m₁+m₂) . v₂, ᵢ
c) v₁, = 2m₁/(m₁+m₂) . v₁, ᵢ + (m₁-m₂)/(m₁+m₂) . v₂, ᵢ
d) v₁, = (m₁+m₂)/(m₁-m₂) . v₁, ᵢ + 2m₂/(m₁+m₂) . v₂, ᵢ

Answer 1

In this problem, when the initial speed of the second object is nonzero, the conservation of momentum can be used to solve for the final speeds of the objects.

Step-by-step explanation:

For this problem, note that v₂ = 0 and use conservation of momentum. Thus, P₁ = P'₁ + P'₂.