Get comprehensive answers to your questions with the help of IDNLearn.com's community. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.
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]
