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A 107 kg boat that is 7 m in length is initially 7.3 m from the pier. A 53 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the turtle. 7.3 m 7 m How far is the child from the pier when she reaches the far end of the boat

Respuesta :

ajeigbeibraheem

Answer:

11.98 m

Explanation:

Given that:

mass of the child [tex]m_c[/tex] = 53 kg

mass of the boat [tex]m_b[/tex] = 107 kg

[tex]\text{length of the boat L = 7 m}[/tex]

the distance of the boat from pies l = 7.3 m

initial momentum [tex]P_i = 0[/tex]

Final momentum [tex]P_f = mc \dfrac{L}{f}- (m_c +m_b) \dfrac{x}{l}[/tex]

where;

x = distance moved by boat towards left

t = time taken for the child to travel to the far end of the boat

[tex]P_i =P_f[/tex]

∴

[tex]m_c \dfrac{L}{t}=(m_c +m_b) \dfrac{x}{t}[/tex]

Then;

[tex]x = \dfrac{m_cL}{m_c+m_b}[/tex]

[tex]x = \dfrac{53 \times 7}{53+107}[/tex]

x = 2.32 m

The distance of the child from the pier is:

d = L +(l - x)

d = 7 m + ( 7.3 m - 2.32 m)

d = 7 m + 4.98 m

d = 11.98 m

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