A scientist launches a 100 g ball from a catapult as part of an experiment. The ball travels at 500 m/s after launch. The catapult weighs 2,000 g and has a slight recoil. Which relationship best describes the recoil of the catapult

V₂ = - m₁ V₁ / m₂

Explanation:

According to law of conservation of momentum, "Total momentum of an isolated system remains constant. i. e

Pi = Pf

We consider ball and catapult an isolated system.

before launching ball momentum of the system is zero.

After launching ball momentum of ball is:

Pb = 0.1 * 500 = 50 kg m/s

Now according to law of conservation of momentum:

Pf = Pi

⇒ Pb + Pc = 0

Let Pb = m₁ V₁

& Pc = m₂ V₂

So

m₁ V₁ + m₂ V₂ = 0

⇒ V₂ = - m₁ V₁ / m₂

The negative sing shows that catapult velocity will have opposite direction to the ball velocity.