A spacecraft of mass M moving with velocity v | vedclass

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Question

(A) According to the principle of conservation of linear momentum,the total initial momentum must equal the total final momentum.Initial momentum $P_i

Vedclass · Accepted Answer

$\frac{Mv}{M - m}$

Vedclass · Answer

(A) According to the principle of conservation of linear momentum,the total initial momentum must equal the total final momentum.Initial momentum $P_i = Mv$.After the explosion,the spacecraft breaks into two pieces of mass $m = M/2$. One piece is stationary $(v_1 = 0)$,and the other piece moves with velocity $v_2$.Final momentum $P_f = m(0) + m(v_2) = m v_2$.Since $m = M/2$,we have $P_f = (M/2)v_2$.Equating initial and final momentum: $Mv = (M/2)v_2$.Solving for $v_2$: $v_2 = 2v$.However,based on the provided options where $m$ is treated as a variable mass component,the conservation equation is $Mv = m(0) + (M - m)v_2$.Thus,$v_2 = \frac{Mv}{M - m}$.

$A$ spacecraft of mass $M$ moving with velocity $v$ suddenly breaks into two pieces of equal mass $m$. After the explosion,one of the masses $m$ becomes stationary. What is the velocity of the other part of the craft?

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