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Max (15 kg) and Maya (12 kg) are ice-skating on a frozen pond. At one moment, when Max is skating away from the shore at 8.2 m/s and Maya is skating towards the shore at 4.6 m/s, they collide and bounce off each other without falling. If Maya rebounds at 3.4 m/s, what is Max’s velocity after their collision?

Respuesta :

boffeemadrid

Answer:

1.8 m/s

Explanation:

[tex]m_1[/tex] = Mass of Max = 15 kg

[tex]m_2[/tex] = Mass of Maya = 12 kg

[tex]u_1[/tex] = Initial velocity of Max = 8.2 m/s

[tex]u_2[/tex] = Initial velocity of Maya = -4.6 m/s

[tex]v_1[/tex] = Final velocity of Max

[tex]v_2[/tex] = Final velocity of Maya = 3.4 m/s

In this system the linear momentum is conserved

[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2\\\Rightarrow v_1=\dfrac{m_1u_1+m_2u_2-m_2v_2}{m_1}\\\Rightarrow v_1=\dfrac{15\times 8.2+12\times -4.6-12\times 3.4}{15}\\\Rightarrow v_1=1.8\ m/s[/tex]

The velocity of Max after their collision is 1.8 m/s