Two astronauts are playing catch in a zero gravitational field. Astronaut 1 of mass m1 is initially moving to the right with spe
ed 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?
The final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut () to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts <em>after throwing the ball</em>.
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, =
Final velocity of the second astronaut, =
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.
if v₂ > v₁, then , to conserve the linear momentum.
Thus, the final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut () 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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