Question

Please Help!!!

Imagine two astronauts working in outer space. Suppose they have equal masses and accidentally run into each other. The first astronaut moves 4.0 m/s to the right before the collision and 1.5 m/s to the left afterwards. If the second astronaut moves 4.0 m/s to the right after the perfectly elastic collision, what was the second astronaut's initial velocity? Hint m1 and m2 are equal, so you do not need them to solve for vzi 1. List your Givens. 2. Show your Work. 3. Give your answer​​

Answer 1

Take "to the right" to be the positive direction. By conservation of momentum,

m₁v₁ + m₂v₂ = m₁(v')₁ + m₂(v')₂

where the v-s denote initial velocities and the v'-s denote final velocities. m₁ and m₂ are of course masses, but we're told that m₁ = m₂, so we can eliminate these factors altogether:

v₁ + v₂ = (v')₁ + (v')₂

We're given that v₁ = +4.0 m/s, (v₁)' = -1.5 m/s, and (v')₂ = +4.0 m/s.

Solve for v₂ :

v₁ + v₂ = (v')₁ + (v')₂

4.0 m/s + v₂ = -1.5 m/s + 4.0 m/s

⇒ v₂ = -1.5 m/s