Question

A 2kg shot is fired from a canon of mass 200kg with a velocity of 50ms with respect to gun. What's the recoil velocity of gun?

Answer 1

Given :

⟶ Mass of bullet = 2kg

⟶ Mass of gun = 200kg

⟶ Velocity of bullet = 50m/s

To Find :

➔ Recoil velocity of gun.

SoluTion :

⟹ Since, no external force acts on the whole system (bullet + gun), we cam easily apply concept of 'momentum conservation' to solve this question.

⟹ Initially, Both (bullet and gun) are at rest position, thus initial momentum of whole system will be zero.

⟹ Momentum is defined as the product of mass of velocity. It is a vector quantity having both magnitude as well as direction.

⟹ SI unit : kg × m/s

$\dashrightarrow\sf\:Initial\:Momentum=Final\:Momentum\\ \\ \dashrightarrow\tt\:0=MV+mv\\ \\ \dashrightarrow\bf\:V=-\dfrac{mv}{M}\\ \\ \dashrightarrow\tt\:V=-\dfrac{2\times 50}{200}\\ \\ \dashrightarrow\tt\:V=-\dfrac{100}{200}\\ \\ \dashrightarrow\underline{\boxed{\bf{V=-0.5\:ms^{-1}}}}\:\gray{\bigstar}$

፨ Note : Negative sign shows opposite direction wrt motion of bullet.