Answer:
The final velocity of the cart is [tex]v_c = 7.02 \ m/s[/tex]
Explanation:
From the question we are told that
The mass of the girl is [tex]m_g = 35.4 \ kg[/tex]
The mass of the cart is [tex]m_c = 15.23 \ kg[/tex]
The speed of the cart and kid(girl) is [tex]v = 4.25 \ m/s[/tex]
The final velocity of the girl is [tex]v_g = 3.06 \ m/s[/tex]
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
[tex]p__{T1}} = (m_g + m_c) * v[/tex]
substituting values
[tex]p__{T1}} = (35.4 + 15.23) * 4.25[/tex]
[tex]p__{T1}} =215.17 \ kg m /s[/tex]
The total momentum after she steps off the back of the cart is mathematically evaluated as
[tex]p__{T2}} = (m_g * v_g ) +( m_c * v_c )[/tex]
Where [tex]v_c[/tex] is the final velocity of the cart
substituting values
[tex]p__{T2}} = (35.4 * 3.06 ) +( 15.23 * v_c )[/tex]
[tex]p__{T2}} = 108. 324 + 15.23 v_c[/tex]
Now according to the law of conservation of momentum
[tex]p__{T1}} =p__{T2}}[/tex]
So
[tex]215.17 \ kg m /s = 108. 324 + 15.23 v_c[/tex]
=> [tex]v_c = 7.02 \ m/s[/tex]
Since the value is positive it implies that the cart moved eastward
