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Answer :
Answer:
(a) [tex]v_g_i=1.08\frac{m}{s}[/tex]
(b) [tex]v_p_i=-0.3\frac{m}{s}[/tex]
Explanation:
According to the law of conservation of momentum:
[tex]\Delta p=0\\p_i=p_f[/tex]
Initially, the girl and the plank are at rest. So, relative to the ice, we have:
[tex]0=m_gv_g_i+m_pv_p_i\\v_p_i=-\frac{m_gv_g_i}{m_p_i}(1)[/tex]
(a) The velocity of the girl relative to the ice is:
[tex]v_g_i=v_g_p+v_p_i(2)[/tex]
Here, [tex]v_g_p[/tex] is the velocity of the girl relative to the plank and [tex]v_p_i[/tex] is the velocity of the plank relative to the ice.
Replacing (1) in (2):
[tex]v_g_i=v_g_p-\frac{m_gv_g_i}{m_p_i}\\v_g_i+\frac{m_gv_g_i}{m_p_i}=v_g_p\\v_g_i(1+\frac{m_g}{m_p})=v_g_p\\v_g_i=\frac{v_g_p}{1+\frac{m_g}{m_p}}\\v_g_i=\frac{1.38\frac{m}{s}}{1+\frac{45kg}{159kg}}\\v_g_i=1.08\frac{m}{s}[/tex]
(b) According to (2), the velocity of the plank relative to the surface of ice is:
[tex]v_p_i=v_g_i-v_g_p\\v_p_i=1.08\frac{m}{s}-1.38\frac{m}{s}\\v_p_i=-0.3\frac{m}{s}[/tex]
The negative sing indicates that the plank is moving to the left.
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