Monument & Energy│Please Help!

Question

Two students are standing face to face on a frozen pond. The left student has a mass of 100 kg and the right student has a mass of 50 kg. If they push off each other what will be true?

1. The right student moves backward faster than the left student
2. They both move back with equal but opposite velocities.
3. The left student moves backward faster than the right student
4. We would need to make more measurements to solve this

Answer 1

m₁ = 100 kg, m₂ = 50 kg

before: total momentum = 0

after: total momentum = m₁v₁ + m₂v₂

Conservation of momentum: 0 = m₁v₁ + m₂v₂

So m₁v₁ = –m₂v₂

which means

v₂ = –(m₁/m₂)v₁ = –(100/50)v₁ = –2v₁

So the student on the right (velocity v₂)

moves backward twice as fast

as the student on the left (velocity v₁)

Answer

The right student moves backward faster than the left student