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?

The final  velocity of the cart is  

Explanation:

From the question we are told that

    The mass of the girl is  

     The mass of the cart is  

      The speed of the cart and  kid(girl) is  

     The final velocity of  the girl is

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

substituting values

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

Where    is the final velocity of the cart

substituting values    

Now according to the law of conservation of momentum

So  

=>      

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

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hope this helps a little