What is the distance between the astronaut and the satellite after 1.0 min?

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In summary, the astronaut, who weighs 80 kg, pushes off a 640 kg satellite with a 100 N force for 0.50 seconds. Due to Newton's 3rd law, the force exerted by the astronaut on the satellite is equal to the force exerted by the satellite on the astronaut. The astronaut travels a distance of 2250 m while the satellite travels a distance of 281.25 m. However, the total distance between them after 1.0 minute is only 42 m, not the 2531 m that was previously calculated. This error was due to using the wrong formula and not accounting for the fact that the acceleration would not continue for the entire minute.
  • #1
Patdon10
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Homework Statement


An 80 kg spacewalking astronaut pushes off a 640 kg satellite, exerting a 100 N force for the 0.50s it takes him to straighten him his arms. How far apart are the astronaut and the satellite after 1.0 min?

2. The attempt at a solution
F = Ma. Two different masses and two different accelerations. Because of Newton's 3rd law we know that the force the astronaut exerts on the satellite is equal to the force the satellite exerts on the astronaut.

F = (80)aastronaut
aastronaut = 1.25 m/s^2

F = 640kg(asatellite
asatellite = 640/100 = 0.156 m/s^2

Distance astronaut travels:
D = (1/2)(1.25)60^2 = 2250 m
D = (1/2)(.156)60^2 = 281.25 m

Total distance I got was ^ = 2531m, which is way wrong.
The correct answer is 42 m. Can anyone point me in the right direction?
 
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  • #2
You applied the equation: D = 1/2 a t^2.

You put in a time of 60 seconds into this formula. After 1/2 sec of initial push, are they still accelerating?
 
  • #3
Ugh...what a stupid mistake. Thanks.
 

Related to What is the distance between the astronaut and the satellite after 1.0 min?

What is Newton's 3rd law of motion?

Newton's 3rd law of motion states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal and opposite force back on the first object.

How does Newton's 3rd law apply to everyday life?

Newton's 3rd law can be seen in many everyday situations, such as when we walk, push a door, or ride a bike. When we take a step, our foot exerts a force on the ground, and the ground exerts an equal and opposite force back on our foot, allowing us to move forward. When we push a door, the door exerts an equal and opposite force back on us, allowing us to open it. And when we ride a bike, the force we exert on the pedals is met with an equal and opposite force from the ground, propelling us forward.

What is an example of a "Newton's 3rd law problem"?

An example of a "Newton's 3rd law problem" would be a rocket launching into space. The rocket exerts a force on the ground, and the ground exerts an equal and opposite force back on the rocket. As the rocket continues to burn fuel and push against the ground, the ground pushes back with an equal and opposite force, eventually allowing the rocket to break free from Earth's gravitational pull and launch into space.

What is the relationship between Newton's 3rd law and Newton's 2nd law?

Newton's 3rd law and Newton's 2nd law are closely related. Newton's 2nd law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the force exerted by one object on another (Newton's 3rd law) will cause an equal and opposite acceleration in the other object, according to Newton's 2nd law.

Do Newton's 3rd law and the law of conservation of momentum contradict each other?

No, Newton's 3rd law and the law of conservation of momentum do not contradict each other. Newton's 3rd law states that the forces between two objects are equal and opposite, while the law of conservation of momentum states that the total momentum of a system remains constant, unless acted upon by an external force. These two laws work together to explain the interaction between objects and the conservation of momentum in a system.

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