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hovering mosquito is hit by a raindrop that is 45 times as massive and falling at 8.1 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic? Express your answer with the appropriate units.

Respuesta :

boffeemadrid

Answer:

7.92 m/s

Explanation:

[tex]m_1[/tex] = Mass of raindrop = [tex]45m_2[/tex]

[tex]m_2[/tex] = Mass of mosquito

[tex]u_1[/tex] = Initial Velocity of raindrop = 8.1 m/s

[tex]u_2[/tex] = Initial Velocity of mosquito = 0 m/s

[tex]v[/tex] = Velocity of center of mass

For elastic collision

[tex]m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow v=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow v=\frac{45m_2\times 8.1 + m_2\times 0}{45m_2 + m_2}\\\Rightarrow v=\frac{364.5m_2}{46m_2}\\\Rightarrow v=7.92\ m/s[/tex]

Hence, the velocity of the attached mosquito, falling immediately afterward is 7.92 m/s

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