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<meta name="description" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<meta property="og:title" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
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<meta property="og:description" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<title>In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.</title>
$1.4.8.$ In case of an elastic impact of a body against a fixed wall, its velocity $v$ changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed $u$ towards the body; b) at a speed $w < v$ in the direction of movement of the body.
<p>The whole point of the problem is to move to an inertial system associated with the wall, correctly describing the relative velocity.</p>
<p>$a)$ In the case when the wall "catches up" with the ball, it is necessary to move to a frame of reference in which the wall is at rest.</p>
<p>In this frame of reference, the relative velocity of the ball before the impact is</p>
<p class="exp">$$v_{0} + u$$</p>
<p>After the elastic impact, the velocity projection changes sign: it becomes equal to </p>
<p class="exp">$$(- v_{0} - u)$$</p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with a velocity of $u$, then the velocity of the ball here is </p>
<p>$b)$ Similarly, we need to go to the frame of reference in which the wall is at rest. </p>
<p>In this frame of reference, the relative velocity of the ball before the impact is $v_{0} - w$. After the elastic impact, the projection of the velocity changes sign: it becomes equal to </p>
<p class="exp">
$$(- v_{0} + w)$$
</p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with the velocity $w$, then the velocity of the ball is </p>
$\begin{aligned}&{a) }\Delta v = -2(v + u).\quad б) \Delta v = -2(v - w). (\text{Projection on the direction of the initial}\\&\text{speeds are considered positive.)}\end{aligned}$
<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="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<meta name="description" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<meta property="og:title" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<meta property="og:title" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<meta property="og:description" content="In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.">
<title>In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.</title>
<title>In case of an elastic impact of a body against a fixed wall, its velocity v changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed u towards the body; b) at a speed w < v in the direction of movement of the body.</title>
$1.4.8.$ In case of an elastic impact of a body against a fixed wall, its velocity $v$ changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed $u$ towards the body; b) at a speed $w < v$ in the direction of movement of the body.
$1.4.8.$ In case of an elastic impact of a body against a fixed wall, its velocity $v$ changes only in the direction. Determine the change after the impact of the velocity of this body, if the wall is moving: a) at a speed $u$ towards the body; b) at a speed $w < v$ in the direction of movement of the body.
<p>The whole point of the problem is to move to an inertial system associated with the wall, correctly describing the relative velocity.</p>
<p>The whole point of the problem is to move to an inertial system associated with the wall, correctly describing the relative velocity.</p>
<p>$a)$ In the case when the wall "catches up" with the ball, it is necessary to move to a frame of reference in which the wall is at rest.</p>
<p>$a)$ In the case when the wall "catches up" with the ball, it is necessary to move to a frame of reference in which the wall is at rest.</p>
<p>In this frame of reference, the relative velocity of the ball before the impact is</p>
<p>In this frame of reference, the relative velocity of the ball before the impact is</p>
<p class="exp">$$v_{0} + u$$</p>
<p class="exp">$$v_{0} + u$$</p>
<p>After the elastic impact, the velocity projection changes sign: it becomes equal to </p>
<p>After the elastic impact, the velocity projection changes sign: it becomes equal to </p>
<p class="exp">$$(- v_{0} - u)$$</p>
<p class="exp">$$(- v_{0} - u)$$</p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with a velocity of $u$, then the velocity of the ball here is </p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with a velocity of $u$, then the velocity of the ball here is </p>
<p>$b)$ Similarly, we need to go to the frame of reference in which the wall is at rest. </p>
<p>$b)$ Similarly, we need to go to the frame of reference in which the wall is at rest. </p>
<p>In this frame of reference, the relative velocity of the ball before the impact is $v_{0} - w$. After the elastic impact, the projection of the velocity changes sign: it becomes equal to </p>
<p>In this frame of reference, the relative velocity of the ball before the impact is $v_{0} - w$. After the elastic impact, the projection of the velocity changes sign: it becomes equal to </p>
<p class="exp">
<p class="exp">
$$(- v_{0} + w)$$
$$(- v_{0} + w)$$
</p>
</p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with the velocity $w$, then the velocity of the ball is </p>
<p>If we then return to the original (laboratory) frame of reference, where the wall moves with the velocity $w$, then the velocity of the ball is </p>
$\begin{aligned}&{a) }\Delta v = -2(v + u).\quad б) \Delta v = -2(v - w). (\text{Projection on the direction of the initial}\\&\text{speeds are considered positive.)}\end{aligned}$
$\begin{aligned}&{a) }\Delta v = -2(v + u).\quad б) \Delta v = -2(v - w). (\text{Projection on the direction of the initial}\\&\text{speeds are considered positive.)}\end{aligned}$
<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>
