Question

A 5 kg cannon ball is loaded into a 300 kg cannon. When the cannon is fired, it recoils at -5 m/s. What is the cannon ball's velocity after the explosion?

Answer 1

300 m/s

Step-by-step explanation:

Answer 2

300m/s

Step-by-step explanation:

The principle of conservation of linear momentum applies to this problem. The total momentum before explosion is equal to the total momentum after the explosion.

Let the mass of the cannon be
`m_c` and the mass of the ball be
`m_b`. According to the principle of conservation of linear momentum the following relationship holds;

`m_cu_c+m_bu_b=m_cv_c+m_bv_b..................(1)`

Since both bodies are at rest before the explosion their initial velocities are zero;
`u_c=0` and
`u_b=0`. Equation (1) then reduces to

`m_cv_c+m_bv_b=0..................(2)`

Which means that,

`-m_cv_c=m_bv_b..................(3)`

Given;

`m_c=300kg\\v_c=-5m/s\\m_b=5kg\\v_b=?`

Substituting all values into equation (3), we obtain the following;

`-300*(-5)=5v_b`

`5v_b=1500\\v_b=(1500)/(5)\\\\v_b=300m/s`