Question

A 35.4 kg girl is riding on the back of a 15.23 kg cart. the cart and the kid are both moving eastward at 4.25 m/s when she steps off the back of the cart. if the final velocity of the girl is 3.06 m/s east ward, what is the final speed of the cart?

Answer 1

Answer:

The final  velocity of the cart is  $v_c = 7.02 \ m/s$

Explanation:

From the question we are told that

    The mass of the girl is  $m_g = 35.4 \ kg$

     The mass of the cart is  $m_c = 15.23 \ kg$

      The speed of the cart and  kid(girl) is  $v = 4.25 \ m/s$

     The final velocity of  the girl is $v_g = 3.06 \ m/s$

Let assume that velocity eastward is  positive and velocity westward is negative (Note that if we assume vise versa it wouldn't affect the answer )

   The total momentum of the system before she steps off the back of the cart

is mathematically evaluated as

        $p__{T1}} = (m_g + m_c) * v$

substituting values

        $p__{T1}} = (35.4 + 15.23) * 4.25$

        $p__{T1}} =215.17 \ kg m /s$

The total momentum after she steps off the back of the cart is mathematically evaluated as

        $p__{T2}} = (m_g * v_g ) +( m_c * v_c )$

Where  $v_c$  is the final velocity of the cart

substituting values    

      $p__{T2}} = (35.4 * 3.06 ) +( 15.23 * v_c )$

       $p__{T2}} = 108. 324 + 15.23 v_c$

Now according to the law of conservation of momentum

       $p__{T1}} =p__{T2}}$

So  

       $215.17 \ kg m /s = 108. 324 + 15.23 v_c$

=>      $v_c = 7.02 \ m/s$

Since the value is positive it implies that the cart moved eastward