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Answer:
B) I₀ = I_f= 0, C) vₐ = [tex]\frac{m_w}{m_a} \ v_w[/tex] , D) t = [tex]\frac{m_a}{m_w} \ \frac{L}{v_w}[/tex]
Explanation:
A) in the attachment you can see a diagram of the movement of the key and the astronaut that is in the opposite direction to each other.
B) Momentum equals the change in momentum in the system
I = ∫ F dt = Δp
since the astronaut has not thrown the key, the force is zero, so the initial impulse is zero
I₀ = 0
The final impulse of the two is still zero, since it is a vector quantity, subtracting the impulse of the two gives zero, since it is an isolated system
I_f = 0
C) We define the system formed by the astronaut and the key, for which the forces during the separation are internal and the moment is conserved
initial instant.
p₀ = 0
final instant
p_f = [tex]m_a v_a - m_w v_w[/tex]
We used the subscript “a” for the astronaut and the subscript “w” for the key
the moment is preserved
po = p_f
0 = mₐ vₐ - m_w v_w
vₐ = [tex]\frac{m_w}{m_a} \ v_w[/tex]
D) as the astronaut goes at constant speed we can use the uniform motion relationships
vₐ = x / t
t = x / vₐ
t = [tex]\frac{m_a}{m_w} \ \frac{L}{v_w}[/tex]
