Respuesta :
Answer:
1.67 m towards right
Explanation:
Let the position of the center of mass of the canoe be at the origin
[tex]m_{c}[/tex] = mass of canoe = 40 kg
[tex]x_{c}[/tex] = position of center of mass of canoe = 0 m
[tex]m_{l}[/tex] = mass of person on left = 50 kg
[tex]x_{l}[/tex] = position of center of mass of person on left = - 1.5 m
[tex]m_{r}[/tex] = mass of person on right = 90 kg
[tex]x_{r}[/tex] = position of center of mass of person on right = 0.5 m
Position of center of mass of the system is given as
[tex]x_{cm} = \frac{m_{c} x_{c} + m_{l} x_{l} + m_{r} x_{r}}{m_{c} + m_{l} + m_{r}} \\x_{cm} = \frac{(40) (0) + (50) (- 1.5) + (90) (0.5)}{40 + 50 + 90} \\x_{cm} = - 0.167 m \\[/tex]
After the two people rearrange their positions, we have
[tex]m_{c}[/tex] = mass of canoe = 40 kg
[tex]x'_{c}[/tex] = position of center of mass of canoe
[tex]m_{l}[/tex] = mass of person on left = 50 kg
[tex]x'_{l}[/tex] = position of center of mass of person on left = - 1 m
[tex]m_{r}[/tex] = mass of person on right = 90 kg
[tex]x'_{r}[/tex] = position of center of mass of person on right = 0.75 m
Position of center of mass of the system remains at the same location and is given as
[tex]x_{cm} = \frac{m_{c} x'_{c} + m_{l} x'_{l} + m_{r} x'_{r}}{m_{c} + m_{l} + m_{r}} \\- 0.167 = \frac{(40) x'_{c} + (50) (- 1.5) + (90) (0.5)}{40 + 50 + 90} \\x'_{c} = 1.502 m[/tex]
Distance traveled by the canoe is given as
[tex]d = x'_{c} - x_{c} = 1.502 - (- 0.167)\\d = 1.67 m[/tex]
direction of movement : towards right.
