A 60kg astronaut (including spacesuit and equipment), is floating at rest a distance of 13 m from the spaceship when she runs out of oxygen and fuel to power her back to the spaceship. She removes her oxygen tank (3.0 kg) and flings it away from the ship at a speed of 15 m/s relative to the ship. Part A At what speed relative to the ship does she recoil toward the spaceship?

To solve this problem it is necessary to apply the concepts related to energy conservation, in which the mass and velocity of the object must be equal to the mass released and the velocity acquired by the astronaut.

The equation given to solve the problem is given by:

[tex]m_1v_1=m_2v_2[/tex]

Where,

[tex]m_1 =[/tex] Mass without tank

[tex]v_1 =[/tex]Velocity of the astronaut

[tex]m_2 =[/tex] Mass removed

[tex]v_2 =[/tex]velocity of the removed mass

Our dates are given by,

[tex]m_1 = 60-3 = 57kg[/tex]

[tex]m_2 = 3kg[/tex]

[tex]v_2 = 15m/s[/tex]

Replacing the values

[tex](57)v_2 = (3)(15)[/tex]

[tex]v_2 = \frac{3*15}{57}[/tex]

[tex]v_2 = 0.78m/s[/tex]

Therefore the speed relative to the spaceship when she try to reach it is 0.78m/s