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<meta name="description" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<title>The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.</title>
$1.4.11.$ The body is dropped over the slab at a height $h$ from it. The slab moves vertically upwards at a speed of $u$. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.
</p>
<h3>Solution</h3>
<p>
<p>Let's move to the reference frame associated with the plate. At the initial moment of time, the relative velocity is $u$ and is directed downwards.</p>
<p>From the law of conservation of energy, we find the velocity of the body $v$ at the moment before the impact</p>
<p class="exp">
$$\frac{mv^2}{2} = \frac{mu^2}{2} + mgh $$
</p>
<p>Where is the desired velocity </p>
<p class="exp">$$v = \sqrt{u^2+2gh}$$</p>
<p>In this inertial reference frame, after an elastic rebound, the relative velocity will only change direction.</p>
<p>A body thrown vertically will land after time</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="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<meta name="description" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<meta property="og:title" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<meta property="og:title" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. 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="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<meta property="og:description" content="The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.">
<title>The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.</title>
<title>The body is dropped over the slab at a height h from it. The slab moves vertically upwards at a speed of u. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.</title>
$1.4.11.$ The body is dropped over the slab at a height $h$ from it. The slab moves vertically upwards at a speed of $u$. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.
$1.4.11.$ The body is dropped over the slab at a height $h$ from it. The slab moves vertically upwards at a speed of $u$. Determine the time between two consecutive impacts of the body on the slab. The blows are absolutely elastic.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>Let's move to the reference frame associated with the plate. At the initial moment of time, the relative velocity is $u$ and is directed downwards.</p>
<p>Let's move to the reference frame associated with the plate. At the initial moment of time, the relative velocity is $u$ and is directed downwards.</p>
<p>From the law of conservation of energy, we find the velocity of the body $v$ at the moment before the impact</p>
<p>From the law of conservation of energy, we find the velocity of the body $v$ at the moment before the impact</p>
<p class="exp">
<p class="exp">
$$\frac{mv^2}{2} = \frac{mu^2}{2} + mgh $$
$$\frac{mv^2}{2} = \frac{mu^2}{2} + mgh $$
</p>
</p>
<p>Where is the desired velocity </p>
<p>Where is the desired velocity </p>
<p class="exp">$$v = \sqrt{u^2+2gh}$$</p>
<p class="exp">$$v = \sqrt{u^2+2gh}$$</p>
<p>In this inertial reference frame, after an elastic rebound, the relative velocity will only change direction.</p>
<p>In this inertial reference frame, after an elastic rebound, the relative velocity will only change direction.</p>
<p>A body thrown vertically will land after time</p>
<p>A body thrown vertically will land after time</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>
