A 44.0-kg girl is standing on a 157-kg plank. Both are originally at rest on a frozen lake, which constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of [tex]1.60 \hat{i} \text{ m/s}[/tex] relative to the plank.

(a) What is the velocity of the plank relative to the ice surface? [tex]\hat{i} \text{ m/s}[/tex]

(b) What is the girl's velocity relative to the ice surface? [tex]\hat{i} \text{ m/s}[/tex]

Question

16-09-2023
Physics

College

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A 44.0-kg girl is standing on a 157-kg plank. Both are originally at rest on a frozen lake, which constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of [tex]1.60 \hat{i} \text{ m/s}[/tex] relative to the plank.

(a) What is the velocity of the plank relative to the ice surface? [tex]\hat{i} \text{ m/s}[/tex]

(b) What is the girl's velocity relative to the ice surface? [tex]\hat{i} \text{ m/s}[/tex]

Answer :

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Paruljain Paruljain · Answer 1 · 2024-12-25T16:58:52-05:00

Final answer:

The velocity of the plank relative to the ice surface is zero m/s. The girl's velocity relative to the ice surface is 1.60 m/s.

Explanation:

To find the velocity of the plank relative to the ice surface, we can use the conservation of momentum. The initial momentum of the system is zero, as both the girl and the plank are at rest. When the girl begins walking, she imparts a forward momentum to the plank. So, the final momentum of the system is the mass of the girl multiplied by her velocity relative to the plank. Since the plank and the ice surface are frictionless, the final momentum of the system is also zero, as there is no external force acting on it. Therefore, the velocity of the plank relative to the ice surface is zero m/s.

The girl's velocity relative to the ice surface can be found by subtracting the velocity of the plank relative to the ice surface (which is zero) from the girl's velocity relative to the plank. Therefore, the girl's velocity relative to the ice surface remains the same as her velocity relative to the plank, which is 1.60 m/s.

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