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Two astronauts are playing catch in a zero gravitational field. Astronaut 1 of mass m1 is initially moving to the right with speed v1 . Astronaut 2 of mass m2 is initially moving to the right with speed v2>v1 . Astronaut 1 throws a ball of mass m with speed u relative to herself in a direction opposite to her motion. Astronaut 2 catches the ball. The final speed of astronaut 1 is vf,1 and the final speed of astronaut 2 is vf,2 .What is the speed vf,1 of astronaut 1 after throwing the ball?

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onyebuchinnaji

The final velocity ([tex]v_1_f[/tex]) of the first astronaut will be greater than the final velocity of the second astronaut ([tex]v_2_f[/tex]) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts after throwing the ball.

The given parameters;

  • Mass of the first astronaut, = m₁
  • Mass of the second astronaut, = m₂
  • Initial velocity of the first astronaut, = v₁
  • Initial velocity of the second astronaut, = v₂ > v₁
  • Mass of the ball, = m
  • Speed of the ball, = u
  • Final velocity of the first astronaut, = [tex]v_f_1[/tex]
  • Final velocity of the second astronaut, = [tex]v_f_2[/tex]

The final velocity of the first astronaut relative to the second astronaut after throwing the ball is determined by applying the principle of conservation of linear momentum.

[tex]m_1v_1 + m_2v_2 = m_2v_2_f + m_1v_1_f[/tex]

if v₂ > v₁, then [tex]v_1_f > v_2_f[/tex], to conserve the linear momentum.

Thus, the final velocity ([tex]v_1_f[/tex]) of the first astronaut will be greater than the final velocity of the second astronaut ([tex]v_2_f[/tex]) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts after throwing the ball.

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