Nastronaut who weighs 800 n on the surface of the earth lifts off from planet zuton in a space ship. the free-fall acceleration on zuton is 3.0 m/s 2 (down). at the moment of liftoff the acceleration of the space ship is 0.50 m/s 2 (up). what is the magnitude of the force of the space ship on the astronaut

0.29 kN

Explanation:

We have the following data:

is the weight of the astronaut on Earth

is the free fall acceleration due gravity on Earth (directed downwards)

is the free fall acceleration due gravity on Zuton (directed downwards)

is the acceleration of the spaceship at litoff (directed upwards)

We have to find the magnitude of the force the space ship exerts on the astronaut.

Firstly, we have to know weight has a direct relation with the mass and the acceleration due gravity. In the case of Earth is:

(1)

Where is the mass of the atronaut.

Isolating :

(2)

(3)

(4)

Now that we know the mass of the astronaut, we can find its weight on Zuton:

(5)

(6)

(7)

Then, we can calculate the force the space ship exerts on the astronaut by the following equation:

(8)

Isolating :

(9)

(10)

(11)

Finally:

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