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Answer :
Answer:
-0.704 m/s
Explanation:
The conservation of momentum demands that since the child + boat + box system is isolated, the initial momentum must equal the final momentum.
Now since initially, everything is at rest, the initial momentum of the system is zero.
The final momentum of the system is
[tex](m_c+m_b)v_1+(m_{\text{box}})v_2[/tex]where
m_c = mass of the child
m_b = mass of the boat
m_box mass of the boat
v1 = belcity of child + boat
v2 = veloctiy of the box.
Equating the initial momentum to the final momentum gives
[tex](m_c+m_b)v_1+(m_{\text{box}})v_2=0[/tex]Now in our case
m_c = 37 kg
m_b = 67 kg
v1 = unknown
m_box = 5.9 kg
v2 = 12.4
Therefore, the above equation gives
[tex](37+67)v_1+(5.9)(12.4)=0[/tex]solving for v1 gives
[tex]v_1=\frac{5.9\cdot12.4}{37+67}[/tex]which evaluates to give (rounded to the nearest hundredth)
[tex]\boxed{v_1=-0.70m/s}[/tex]which is our answer!
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