Question

A 20-kg child is coasting at 3.3 m/s over flat ground in a 4.0-kg wagon. The child drops a 1.0-kg ball out the back of the wagon. What is the final speed of the child and wagon?

Answer 1

Answer:

The final velocity is $u_f = 3.44 \ m/s$

Explanation:

From the question we are told that

    The mass of the child is  $m_1 = 20 \ kg$

    The initial  speed  of the child is  $u_1 = 3.3 \ m/s$

    The mass of the wagon is  $m_w = 4.0 \ kg$

    The  initial  speed of the wagon is $u_w = 3.3 \ m/s$

    The mass of the ball is  $m_2 = 1.0 \ kg$

    The initial speed off the ball  is  $u_2 = 3.3 \ m/s$

Generally the initial  speed of the system (i.e the child , wagon ,  ball) is  

          $u_1 = u_w = u_2 = u =3.3 \ m/s$

Generally from the law of linear momentum conservation

    $p_i = p_f$

Here $p_i$  is the momentum of the system before the ball is dropped which is mathematically represented  as

      $p_i = ( m_1 + m_2 + m_3 ) * u$

=>   $p_i = ( 20 + 4 + 1 ) * 3.3$

=>   $p_i = 82.5 \ kg \cdot m/s$

and  

       $p_f$  is the momentum of the system after the ball is dropped which is mathematically represented  as  

       $p_f = ( m_1 + m_w ) * u_f$

=>   $p_i = ( 20 + 4 ) * u_f$

So

     $82.5 = 24 * u_f$

=>   $u_f = 3.44 \ m/s$