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A 45.0-kg girl is standing on a 147-kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.53 m/s to the right relative to the plank.

(Let the direction the girl is moving in be positive. Indicate the direction with the sign of your answer.)

Calculate the velocity of the plank.

Answer :

Answer:

[tex]v_1 = 1.17 m/s[/tex]

Explanation:

given,

mass of the girl (m₁)= 45 kg

mass of the plank(m₂) = 147 kg

constant velocity of girl relative to plank = 1.53 m/s

velocity relative to ice berg(v₁) = ?

conservation of momentum

momentum of system = 0

[tex]m_1v_1 = m_2v_2[/tex]

[tex]45 \times v_1 = 147 \times (1.53 - v_1)[/tex]

[tex]45v_1 = 224.91 - 147 v_1[/tex]

[tex]192 v_1 = 224.91[/tex]

[tex]v_1 = \dfrac{224.91}{192}[/tex]

[tex]v_1 = 1.17 m/s[/tex]

hence, the velocity relative to ice berg is 1.17 m/s

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