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<meta name="description" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
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<meta property="og:description" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<title>A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.</title>
$1.4.14.$ A nucleus traveling at speed $v$ splits into two identical fragments. Determine the maximum possible angle $\alpha$ between the velocities of one of the fragments and the vector $v$, if the fragments have a velocity $u < v$ during the decay of a resting nucleus.
</p>
<h3>Solution</h3>
<p>
<p>The velocity and one of the accelerations of the nucleus are</p>
<p>where $\vec{v}_{0}$ is its velocity before the decay of the nucleus, $\vec{v}$ is the velocity of the fragment relative to the resting nucleus (that is, in the coordinate system in which the nucleus was at rest before the decay).</p>
<p>Let's arrange the vector $\vec{v}_{0}$ as shown in the figure. The end of the vector can lie on a circle of radius $| \vec{v} |$. </p>
<p>It is clear from the figure that the vector and forms the maximum angle $\alpha$ with the vector $\vec{v}_{0}$ if the angle between the vectors $\vec{u}$ and $\vec{v}$ is $\pi / 2 $. In this case</p>
<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="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<meta name="description" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<meta property="og:title" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<meta property="og:title" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<meta property="og:description" content="A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.">
<title>A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.</title>
<title>A nucleus traveling at speed v splits into two identical fragments. Determine the maximum possible angle \alpha between the velocities of one of the fragments and the vector v, if the fragments have a velocity u < v during the decay of a resting nucleus.</title>
$1.4.14.$ A nucleus traveling at speed $v$ splits into two identical fragments. Determine the maximum possible angle $\alpha$ between the velocities of one of the fragments and the vector $v$, if the fragments have a velocity $u < v$ during the decay of a resting nucleus.
$1.4.14.$ A nucleus traveling at speed $v$ splits into two identical fragments. Determine the maximum possible angle $\alpha$ between the velocities of one of the fragments and the vector $v$, if the fragments have a velocity $u < v$ during the decay of a resting nucleus.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>The velocity and one of the accelerations of the nucleus are</p>
<p>The velocity and one of the accelerations of the nucleus are</p>
<p>where $\vec{v}_{0}$ is its velocity before the decay of the nucleus, $\vec{v}$ is the velocity of the fragment relative to the resting nucleus (that is, in the coordinate system in which the nucleus was at rest before the decay).</p>
<p>where $\vec{v}_{0}$ is its velocity before the decay of the nucleus, $\vec{v}$ is the velocity of the fragment relative to the resting nucleus (that is, in the coordinate system in which the nucleus was at rest before the decay).</p>
<p>Let's arrange the vector $\vec{v}_{0}$ as shown in the figure. The end of the vector can lie on a circle of radius $| \vec{v} |$. </p>
<p>Let's arrange the vector $\vec{v}_{0}$ as shown in the figure. The end of the vector can lie on a circle of radius $| \vec{v} |$. </p>
<p>It is clear from the figure that the vector and forms the maximum angle $\alpha$ with the vector $\vec{v}_{0}$ if the angle between the vectors $\vec{u}$ and $\vec{v}$ is $\pi / 2 $. In this case</p>
<p>It is clear from the figure that the vector and forms the maximum angle $\alpha$ with the vector $\vec{v}_{0}$ if the angle between the vectors $\vec{u}$ and $\vec{v}$ is $\pi / 2 $. In this case</p>
<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>
