Answer :
Final answer:
The velocity of the plank relative to the ice surface is approximately -0.443 m/s, and the girl's velocity relative to the ice surface is approximately 1.42 m/s.
Explanation:
To find the velocity of the plank relative to the ice surface, we can use the law of conservation of momentum. The initial momentum of the system is zero since both the girl and the plank are at rest. When the girl starts walking, she imparts a forward momentum to the plank.
Let's denote the velocity of the plank relative to the ice surface as vp and the velocity of the girl relative to the ice surface as vg.
According to the law of conservation of momentum, the total momentum before and after the girl starts walking must be equal.
Before the girl starts walking, the total momentum is zero:
0 = (mass of girl) * (velocity of girl) + (mass of plank) * (velocity of plank)
Since the girl and the plank are initially at rest, their velocities are both zero.
After the girl starts walking, the total momentum is:
0 = (mass of girl) * (velocity of girl) + (mass of plank) * (velocity of plank)
Substituting the given values:
0 = (44.6 kg) * (1.421 m/s) + (143 kg) * (velocity of plank)
Solving for velocity of plank:
velocity of plank = -((44.6 kg) * (1.421 m/s)) / (143 kg)
Calculating the value:
velocity of plank ≈ -0.443 m/s
Therefore, the velocity of the plank relative to the ice surface is approximately -0.443 m/s.
To find the girl's velocity relative to the ice surface, we can use the same equation:
0 = (mass of girl) * (velocity of girl) + (mass of plank) * (velocity of plank)
Substituting the given values:
0 = (44.6 kg) * (velocity of girl) + (143 kg) * (-0.443 m/s)
Solving for velocity of girl:
velocity of girl = ((143 kg) * (0.443 m/s)) / (44.6 kg)
Calculating the value:
velocity of girl ≈ 1.42 m/s
Therefore, the girl's velocity relative to the ice surface is approximately 1.42 m/s.
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