Question

an 80.0 kg astronaut carrying a 15.0 kg tool kit is drifting away from the space station at a speed of 1.25 m/s. a) if she throws the tool kit away from the space station with a speed of 6.00 m/s, what is her final speed and direction?

Answer 1

The final speed of the astronaut at the space station is 0.36 m/s and the direction will be opposite to the direction of the tool kit thrown.

The mass of the astronaut = 80 kg

The mass of the tool kit = 15 kg

The speed of the space station = 1.25 m/s

The speed of the tool kit threw = 6 m/s

The final speed of the astronaut can be found using the conservation of momentum formula,

           $\displaystyle m_{1}v_{f1} + m_{2}v_{f2} = m_{1}v_{i1} + m_{2}v_{i2}$

where m₁ is the mass of the astronaut

           m₂ is the mass of the tool kit

           $\displaystyle v_{i1}$ and $\displaystyle v_{i2}$ is the speed of the space station

           $\displaystyle v_{f1}$ is the speed of the astronaut after throwing the toolkit

Let us substitute the known values in the above equation, we get

              (80 x $\displaystyle v_{f1}$) + (15 x 6) = (80 x 1.25) + (15 x 1.25)

                     (80 x $\displaystyle v_{f1}$) + 90 = 100 + 18.75

                              80 x $\displaystyle v_{f1}$   = 118.75 - 90

                                80 x $\displaystyle v_{f1}$ = 28.75

                                        $\displaystyle v_{f1}$ = 28.75 / 80

                                              = 0.36 m/s

Therefore, the final speed of the astronaut is 0.36 m/s

By newton's third law, for every action, there will be an equal and opposite reaction. Thus, the direction of the astronaut's direction will be against the direction of the tool kit thrown.

Learn more about the conservation of momentum in

brainly.com/question/2456421

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