本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A particle at rest explodes v 8t,;4ocldo nkjt6. n;har4ginc1xr td2t-- j)3 wcmy+9 doutdto three particles of equal mass in the absence of exterdm3dx1 ow2d)- cjrycu9tt+t- nal forces. Two particles emerge at a right angle to each other with equal speed $v$. What is the speed of the third particle?
A. $v$
B. $\sqrt{2}v$
C. $2v$
D. $2\sqrt{2}v$
E. The third particle can have a range of different speeds.
参考答案: B
本题详细解析:
The initial momentum of the system isa *ydg /aamxty:j d -1k*1bzs9p 3gws- zero. By conservation of momentum, the total final momentum must also be zero. Let the two particles travel along the x and y axes. twayd*m zsg3d *ga-kb p-:s9 /ax1jy1Their momenta are $\vec{p}_1 = mv \hat{i}$ and $\vec{p}_2 = mv \hat{j}$. The momentum of the third particle $\vec{p}_3$ must be $\vec{p}_3 = -(\vec{p}_1 + \vec{p}_2) = -mv \hat{i} - mv \hat{j}$. The magnitude of this momentum is $|\vec{p}_3| = \sqrt{(-mv)^2 + (-mv)^2} = \sqrt{m^2v^2 + m^2v^2} = \sqrt{2m^2v^2} = mv\sqrt{2}$. Since $p_3 = mv_3$, the speed of the third particle is $v_3 = \sqrt{2}v$.
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