<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:title" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:image" content="img/logo.png">
<meta property="og:description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<title>The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?</title>
The radioactive core decayed into three fragments of mass $m_1$, $m_2$, and $m_3$, having mutually perpendicular velocities $v_1$, $v_2$, and $v_3$, respectively. What was the speed of the nucleus before the decay?
Since velocity's vectors are mutually perpendicular, their directions can be fundamental for establishing the spatial coordinated system. So, let be $\hat{v_1}$, $\hat{v_2}$ and $\hat{v_3}$ the unitary vectors for each direction. Applying MCL for each direction,
−
$$(m_1+m_2+m_3)V_1 = m_1v_1 \;(1)$$
−
$$(m_1+m_2+m_3)V_2 = m_2v_2 \;(2)$$
−
$$(m_1+m_2+m_3)V_3 = m_3v_3 \;(3)$$
+
$$(m_1+m_2+m_3)V_1 = m_1v_1 \quad(1)$$
+
$$(m_1+m_2+m_3)V_2 = m_2v_2 \quad(2)$$
+
$$(m_1+m_2+m_3)V_3 = m_3v_3 \quad(3)$$
where $V_1$, $V_2$ and $V_3$ are the components of velocity $\vec{V}$,
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta name="description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:title" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:title" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
<meta property="og:description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<meta property="og:description" content="The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?">
<title>The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?</title>
<title>The radioactive core decayed into three fragments of mass m_1, m_2, and m_3, having mutually perpendicular velocities v_1, v_2, and v_3, respectively. What was the speed of the nucleus before the decay?</title>
The radioactive core decayed into three fragments of mass $m_1$, $m_2$, and $m_3$, having mutually perpendicular velocities $v_1$, $v_2$, and $v_3$, respectively. What was the speed of the nucleus before the decay?
The radioactive core decayed into three fragments of mass $m_1$, $m_2$, and $m_3$, having mutually perpendicular velocities $v_1$, $v_2$, and $v_3$, respectively. What was the speed of the nucleus before the decay?
Since velocity's vectors are mutually perpendicular, their directions can be fundamental for establishing the spatial coordinated system. So, let be $\hat{v_1}$, $\hat{v_2}$ and $\hat{v_3}$ the unitary vectors for each direction. Applying MCL for each direction,
Since velocity's vectors are mutually perpendicular, their directions can be fundamental for establishing the spatial coordinated system. So, let be $\hat{v_1}$, $\hat{v_2}$ and $\hat{v_3}$ the unitary vectors for each direction. Applying MCL for each direction,
$$(m_1+m_2+m_3)V_1 = m_1v_1 \;(1)$$
$$(m_1+m_2+m_3)V_1 = m_1v_1 \quad(1)$$
$$(m_1+m_2+m_3)V_2 = m_2v_2 \;(2)$$
$$(m_1+m_2+m_3)V_2 = m_2v_2 \quad(2)$$
$$(m_1+m_2+m_3)V_3 = m_3v_3 \;(3)$$
$$(m_1+m_2+m_3)V_3 = m_3v_3 \quad(3)$$
where $V_1$, $V_2$ and $V_3$ are the components of velocity $\vec{V}$,
where $V_1$, $V_2$ and $V_3$ are the components of velocity $\vec{V}$,
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
