Answer:
119.74437 kg
Explanation:
Mass of astronaut = x
Mass of chair = 42.5 kg
Time period is given by
[tex]T=2\pi\sqrt{\dfrac{m}{k}}[/tex]
So,
[tex]T\propto \sqrt{m}[/tex]
[tex]\\\Rightarrow \dfrac{T_1}{T_2}=\sqrt{\dfrac{m_1}{m_2}}\\\Rightarrow \dfrac{1.3}{2.54}=\sqrt{\dfrac{42.5}{42.5+x}}\\\Rightarrow \dfrac{1.3^2}{2.54^2}=\dfrac{42.5}{42.5+x}\\\Rightarrow 42.5+x=\dfrac{42.5\times 2.54^2}{1.3^2}\\\Rightarrow x=\dfrac{42.5\times 2.54^2}{1.3^2}-42.5\\\Rightarrow x=119.74437\ kg[/tex]
The mass of the astronaut is 119.74437 kg is the required answer.
