A 92-kg fullback moving south with a speed of 5.8 m/s is tackled by a 110-kg lineman running north with a speed of 3.6 m/s. Assuming momentum conservation, determine the speed and direction of the two players immediately after the tackle.Give the direction as an angle, in degrees, south of west.

We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two players must be conserved before and after they collide.

Mathematically:

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1+m_2)v[/tex]

where, taking north as positive direction:

[tex]m_1 = 92 kg[/tex] is the mass of the first player

[tex]u_1 = -5.8 m/s[/tex] is the initial velocity of the first player (south, so negative)

[tex]m_2 = 110 kg[/tex] is the mass of the second player

[tex]u_2 = 3.6 m/s[/tex] is the initial velocity of the second player (north, so positive)

[tex]v[/tex] is the final combined velocity of the two players

Solving for v, we find the final velocity of the two players combined:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1+m_2}=\frac{(92)(-5.8)+(110)(3.6)}{92+110}=-0.68 m/s[/tex]

where the negative sign indicates their final direction is south.

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