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<meta name="description" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
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<meta property="og:description" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<title>A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.</title>
$1.4.12.$ A body flies horizontally at speed $v$ into the space between two vertical walls that move at speed $u$. Determine the speed of the body after the $n$-th impact on the front wall. Distance between walls $L$. The blows are absolutely elastic.
<p>Let's consider how the velocity $v_x$ changes along the horizontal axis $Ox$</p>
<p>When the body flies to the right wall, $v_x = v$. Then, after an elastic collision, the velocity changes to $v_x = v - 2u$. For more details on why this happens, see <a href="../1.4.9" target="_blank">1.4.9</a>.</p>
<p>Similarly, after hitting the left wall, $v_x$ will be equal to </p>
<p class="exp">$$v_x = (v - 2u) + 2u = v$$</p>
<p>Thus, always after hitting the right wall, the speed of $v_x$ will be equal to $v - 2u$</p>
$$\fbox{$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$}$$
</p>
</p>
<h4>Answer</h4>
<p>
The projection of the velocity on the horizontal direction $v_x = v −2u$; the projection of the velocity on the vertical direction $$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$$
<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 body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<meta name="description" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<meta property="og:title" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<meta property="og:title" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<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 body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<meta property="og:description" content="A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.">
<title>A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.</title>
<title>A body flies horizontally at speed v into the space between two vertical walls that move at speed u. Determine the speed of the body after the n-th impact on the front wall. Distance between walls L. The blows are absolutely elastic.</title>
$1.4.12.$ A body flies horizontally at speed $v$ into the space between two vertical walls that move at speed $u$. Determine the speed of the body after the $n$-th impact on the front wall. Distance between walls $L$. The blows are absolutely elastic.
$1.4.12.$ A body flies horizontally at speed $v$ into the space between two vertical walls that move at speed $u$. Determine the speed of the body after the $n$-th impact on the front wall. Distance between walls $L$. The blows are absolutely elastic.
<p>Let's consider how the velocity $v_x$ changes along the horizontal axis $Ox$</p>
<p>Let's consider how the velocity $v_x$ changes along the horizontal axis $Ox$</p>
<p>When the body flies to the right wall, $v_x = v$. Then, after an elastic collision, the velocity changes to $v_x = v - 2u$. For more details on why this happens, see <a href="../1.4.9" target="_blank">1.4.9</a>.</p>
<p>When the body flies to the right wall, $v_x = v$. Then, after an elastic collision, the velocity changes to $v_x = v - 2u$. For more details on why this happens, see <a href="../1.4.9" target="_blank">1.4.9</a>.</p>
<p>Similarly, after hitting the left wall, $v_x$ will be equal to </p>
<p>Similarly, after hitting the left wall, $v_x$ will be equal to </p>
<p class="exp">$$v_x = (v - 2u) + 2u = v$$</p>
<p class="exp">$$v_x = (v - 2u) + 2u = v$$</p>
<p>Thus, always after hitting the right wall, the speed of $v_x$ will be equal to $v - 2u$</p>
<p>Thus, always after hitting the right wall, the speed of $v_x$ will be equal to $v - 2u$</p>
$$\fbox{$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$}$$
$$\fbox{$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$}$$
</p>
</p>
</p>
</p>
<h4>Answer</h4>
<h4>Answer</h4>
<p>
<p>
The projection of the velocity on the horizontal direction $v_x = v −2u$; the projection of the velocity on the vertical direction $$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$$
The projection of the velocity on the horizontal direction $v_x = v −2u$; the projection of the velocity on the vertical direction $$v_y = (2n − 1)g L \frac{2(v-u)}{v(v-2u)}$$
<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>
