Respuesta :
Answer:
1.3m/s to the west.
Explanation:
Since there are no external forces acting in the horizontal axis (the gravitational force doesn't count as it is in the vertical axis), the linear momentum must be conserved. This is, that the momentum of the system at the instant in which the fisherman jumped has to be equal to the momentum after the fisherman landed on the boat. So, this can be expressed as:
[tex]m_{F}v_{F0}+m_{B}v_{B0}=(m_{F}+m_{B})v_{f}[/tex]
But the initial speed of the boat [tex]v_{B0}[/tex] is zero because it starts at rest. Then, we get:
[tex]m_{F}v_{F0}=(m_{F}+m_{B})v_{f}[/tex]
Solving for the final velocity of the fisherman and the boat [tex]v_f[/tex], we have:
[tex]v_f=\frac{m_{F}v_{F0}}{m_{F}+m_{B}} \\\\v_f=\frac{(86kg)(3.5m/s)}{86kg+134kg}=1.3m/s[/tex]
Finally, since the final velocity has the same sign as the initial velocity, it may go in the same direction. Thus, the final velocity of the fisherman and the boat is 1.3m/s to the west.
