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A 98kg Florida running back is running to the right at 6 m/s toward the Oklahoma goal line. The running back is hit by a 118kg Oklahoma linebacker running to the left at 4 m/s. (a) What is the momentum of each player? (b) What is the net momentum of the two players after the collision? (c) If the two players entangle and continue traveling as a single unit following the collision, what is their combined velocity? (Show all calculations)

Respuesta :

Answer:

a) 588 kg m/s, -472 kg m/s

b) 116 kg m/s

c) 0.53 m/s

Explanation:

[tex]m_1[/tex] = Mass of Florida player = 98 kg

[tex]m_2[/tex] = Mass of Oklahoma player = 118 kg

[tex]u_1[/tex] = Initial Velocity of Florida player = 6 m/s

[tex]u_2[/tex] = Initial Velocity of Oklahoma player = -4 m/s

[tex]v[/tex] = Combined Velocity

a) Momentum of Florida player

[tex]p=m_u_1\\\Rightarrow p=98\times 6\\\Rightarrow p=588 kg m/s[/tex]

Momentum of Oklahoma player

[tex]p=m_2u_2\\\Rightarrow p=118\times -4\\\Rightarrow p=-472 kg m/s[/tex]

b)

[tex]p=588-472\\\Rightarrow p=116 kg m/s[/tex]

Net momentum of the players is 116 kgm/s

c)

[tex]m_1u_1 + m_2u_2 =(m_1 + m_2)v_c\\\Rightarrow v_c=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow v=\frac{116}{98 + 118}\\\Rightarrow v=0.53\ m/s[/tex]

The combined velocity will be 0.53 m/s

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