a 60-kilogram astronaut floating in space outside the capsule throws his 0.50-kilogram hammer such that it moves with a speed of 10 m/s relative to the capsule. what happens to the astronaut?
When the astronaut throws the hammer, according to Newton's Third Law of Motion, there will be an equal and opposite reaction. As a result, there will be a forward thrust on the astronaut in the opposite direction of the hammer's throw.
To determine the velocity of the astronaut after throwing the hammer, we can use the principle of conservation of momentum. The total momentum before throwing the hammer is zero since the astronaut and the hammer are initially at rest. After throwing the hammer, the total momentum should remain zero because no external forces are acting on the system. Since momentum is a vector quantity, we need to take into account both the magnitude and direction.
Let's denote the initial velocity of the astronaut as V1 and the final velocity after throwing the hammer as V2. The mass of the astronaut is 60 kilograms, and the mass of the hammer is 0.50 kilograms. The hammer's velocity relative to the capsule is given as 10 m/s.
Using the conservation of momentum, we can write:
Initial momentum of the astronaut (before throwing the hammer) = Final momentum of the astronaut (after throwing the hammer)
(Mass of astronaut x Initial velocity of astronaut) + (Mass of hammer x Initial velocity of hammer) = (Mass of astronaut x Final velocity of astronaut) + (Mass of hammer x Final velocity of hammer)
(60 kg x V1) + (0.50 kg x 0 m/s) = (60 kg x V2) + (0.50 kg x 10 m/s)
60V1 = 60V2 + 5
Since the hammer is thrown with a velocity of 10 m/s relative to the capsule, we can express the hammer's velocity relative to the astronaut as (V2 - 0). This simplifies the equation to:
60V1 = 60(V2 - 10) + 5
Solving for V2:
60V1 = 60V2 - 600 + 5
55 = 60V2 - 60V1
V2 - V1 = 55/60
V2 - V1 = 11/12
So, the astronaut's velocity after throwing the hammer (V2) will be 11/12 of the difference between the hammer's velocity relative to the capsule and the astronaut's initial velocity (V1).
To determine the direction of the astronaut's motion, we need to consider the sign of V2 - V1. If the result is positive, the astronaut moves in the same direction as the hammer. If the result is negative, the astronaut moves in the opposite direction to the hammer.
Therefore, the astronaut will move in the opposite direction to the thrown hammer, with a velocity slightly less than that of the hammer.