Respuesta :
Answer:
100kg
Explanation:
Momentum is defined as the product of mass times velocity:
[tex]p=mv[/tex]
The total momentum M must be equal to the sum of momentums of the system components, in this case the momentum of the lady plus the momentum of the cart:
[tex]M=m_{woman}v_{woman}+m_{cart}v_{cart}[/tex]
since both the woman and the shopping cart have the same velocity:
[tex]v_{woman}=v_{cart}=v[/tex]
the equation becomes:
[tex]M=m_{woman}v+m_{cart}v\\M=v(m_{woman}+m_{cart})[/tex]
and since we need the mass of the cart we solve for [tex]m{cart}[/tex]:
[tex]m_{woman}+m_{cart}=\frac{M}{v} \\\\m_{cart}=\frac{M}{v} -m_{woman}[/tex]
the values given by the problem are the following:
total momentum: [tex]M=450kgm/s[/tex]
mass of the woman: [tex]m_{woman}=50kg[/tex]
velocity: [tex]v=3m/s[/tex]
we substitute all of them in the equation to find the mass of the shopping cart:
[tex]m_{cart}=\frac{450kgm/s}{3m/s} -50kg\\\\m_{cart}=150kg-50kg\\\\m_{cart}=100kg[/tex]
the mass of the cart is 100kg.
