Answer:
It will take the astronaut 239.55 seconds to get to the ship after he has thrown the wrench.
Explanation:
The astronaut and the wrench are an isolated system; therefore, the law of conservation of momentum applies:
[tex]M_wv_w = M_a v_a[/tex],
where, [tex]M_w[/tex],[tex]v_w[/tex] and [tex]M_a,v_a[/tex] are the mass & velocity of the the wrench and he astronaut respectively.
Putting in numbers we get:
[tex](0.613kg)(24.9) = (89.4kg)v_a[/tex]
[tex]v_a = \dfrac{(0.613kg)(24.9)}{89.4kg}[/tex]
[tex]v_a = 0.171m/s[/tex]
which is the velocity of the astronaut.
With this velocity, the time it takes the astronaut to cover a distance of 40.6 will be
[tex]t = \dfrac{40.0m}{0.171m/s}[/tex]
[tex]\boxed{t = 239.55 s}[/tex]
Thus, it will take the astronaut 239.55 seconds to get to the ship after he has thrown the wrench.
P.S: we discounted the constant velocity of the ship because the astronaut was at rest relative to it (he was moving at the same velocity)
