Mastering the Conservation of Momentum: A Journey Back to Safety

How do we calculate the time it takes to return to the space station after throwing a tool-bag?

a. 10 seconds

b. 32 seconds

c. 4 seconds

d. 25 seconds

Theoretical Calculation:

The actual time it takes you to reach the station safely is 40 seconds, which is longer than any of the options given. To solve this problem, we can use the conservation of momentum principle.

When faced with a challenging situation in space, understanding the concept of conservation of momentum is crucial for your survival. In this scenario, when your safety rope comes loose while making repairs outside the international space station, you are left floating 20 meters away from safety. Desperately needing to return, you throw your 10 kg tool-bag away from the space station in order to propel yourself back.

According to Newton's third law of motion, the force exerted by the bag on you is equal in magnitude and opposite in direction to the force you exert on the bag. By applying the principle of the conservation of momentum, we can calculate the final velocity of the combined system (you and the bag) after the throw.

After throwing the bag, your velocity relative to the space station is 0.5 m/s in the direction opposite to the bag's velocity. Utilizing the formula d = vt, where d is the distance you need to cover to reach the station (20 meters) and v is your velocity relative to the station (0.5 m/s), we find that it takes you 40 seconds to return safely.

Remember, in the vastness of space, every action has an equal and opposite reaction. By mastering the laws of physics, you can navigate through challenges and overcome obstacles, ensuring your safe return to the station.