Question

At the range Mr. Romeo tests his gun to be shooting at 90 m/s. The mass of a paintball is 30 grams. The mass of his gun is 6 kg. What speed is his gun recoiling at?

Answer 1

`0.45 \ "m/s"`

Explanation:

I would use the law of conservation of momentum, which states that,

`p_"initial"=p_"final"`

`=>m_1v_1=m_2v_2`

So, we get:

`0.03 \ "kg"*90 \ "m/s"=6 \ "kg"*v_2`

`v_2=(0.03color(red)cancelcolor(black)"kg"*90 \ "m/s")/(6color(red)cancelcolor(black)"kg")`

`=0.45 \ "m/s"`

Of course, this is not the exact value, as this assumes that no other forces act on the gun, but when it is recoiling, there is also air resistance, and so the expected value would be lower.