Question

An 880 kg cannon at rest fires a 12.4 kg cannonball forward at 540 m/s. What is the recoil velocity of the cannon

Answer 1

The recoil velocity of the cannon is 7.61 m/s in the opposite direction of the cannonball

Step-by-step explanation:

Linear Momentum

The principle of conservation of the linear momentum establishes that the sum of the linear momentums of every object in an isolated system (no external forces) is constant, regardless of the interactions between them.

Let's think we have two objects with masses
`m_1` and
`m_2`, moving at speeds
`v_1` and
`v_2`. If they collide and change their speeds to
`v_1'` and
`v_2'`, then

`m_1v_1+m_2v_2=m_1v_1'+m_2v_2'`

In our problem, the 880 kg cannon is initially at rest and has the cannonball of 12.4 Kg inside of it. As the initial speed of both joined objects is zero, the initial total momentum is zero. After the ball is fired, the ball moves at v_2=540 m/s. We need to find the recoil velocity of the cannon
`v_1'`

`m_1v_1'+m_2v_2'=0`

`\displaystyle m_1v_1'=-m_2v_2'`

`\displaystyle v_1'=-(m_2v_2')/(m_1)`

`\displaystyle v_1'=-(12.4(540))/(880)=-7.61\ m/s`

The recoil velocity of the cannon is 7.61 m/s in the opposite direction of the cannonball