An astronaut and his space suit have a combined mass of 157 kg. The astronaut is using a 5 kg tqol kit to repair a solar panel on the International
Space Station. When the têther connecting the astronaut to the space
station becomes unattached, the astronaut, still holding the tool kit, starts
to float away at 0.2 m/s. Calculate the velocity with which the astronaut
must throw the tool kit in order to float back toward the space station at
0.1 m/s. Show your calculations and include units in your answer.
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The velocity with which the astronaut must throw the tool kit is 9.62 m/s.

The given parameters:

Apply the principle of conservation of linear momentum to determine the velocity of the tool kit;

Thus, the velocity with which the astronaut must throw the tool kit is 9.62 m/s.

Learn more about conservation of linear momentum here: link

v₃ = 9.62[m/s]

Explanation:

To solve this type of problem we must use the principle of conservation of linear momentum, which tells us that the momentum is equal to the product of mass by velocity.

We must analyze the moment when the astronaut launches the toolkit, the before and after. In order to return to the ship, the astronaut must launch the toolkit in the opposite direction to the movement.

Let's take the leftward movement as negative, which is when the astronaut moves away from the ship, and rightward as positive, which is when he approaches the ship.

In this way, we can construct the following equation.

where:

m₁ = mass of the astronaut = 157 [kg]

m₂ = mass of the toolkit = 5 [kg]

v₁ = velocity combined of the astronaut and the toolkit before throwing the toolkit = 0.2 [m/s]

v₂ = velocity for returning back to the ship after throwing the toolkit [m/s]

v₃ = velocity at which the toolkit should be thrown [m/s]

Now replacing:

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2