Question

A 35 Kg boy jumps (from rest) into a moving trolley of mass 70 kg and already
moving at a velocity of 5 m/s to the right. What is the speed of the trolley after the
boy has jumped in? ​

Answer 1

Answer:

We have two items: the boy and the trolley. 

interaction is when the boy jumps onto the trolley. 

Let v1i and v2i be the velocities of the boy and the trolley before the boy jumps in (initial velocities) 

     v1i = 0 and v2i = 5 m/s 

The moment Pi of the system boy-trolley before the jump 

     pi = moment of boy + moment of trolley = 35 × 0 + 70 × 5 = 350 Kg m/s 

Let v be the velocity of the trolley (with the boy in it) , the momentum of the trolley is 

     p = (35 + 70) v 

Conservation of momentum 

     350 = (35 + 70) v 

     v = 350 / 105 = 3.3 m/s to the right.

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Answer 2

Answer:

Let v1i and v2i be the velocities of the boy and the trolley before the boy jumps in (initial velocities)  

    v1i = 0 and v2i = 5 m/s  

The moment Pi of the system boy-trolley before the jump  

    pi = moment of boy + moment of trolley = 35 × 0 + 70 × 5 = 350 Kg m/s  

Let v be the velocity of the trolley (with the boy in it) , the momentum of the trolley is  

    p = (35 + 70) v  

Conservation of momentum  

    350 = (35 + 70) v  

    v = 350 / 105 = 3.3 m/s to the right.

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