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<meta name="description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
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<meta property="og:description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<title>A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.</title>
$1.3.7.$ A ball is launched along a smooth inclined plane at a speed of $v$. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of $45^\circ$ . The initial velocity of the ball forms an angle of $45^\circ$ with the horizontal edge of the plane.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem $1.3.7$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
</p>
<center>
<figure>
<img src="drawing.png"
loading="lazy" width="230" />
<figcaption>
Effective acceleration of free fall ($g^*$)
</figcaption>
</figure>
</center>
<p>
On an inclined plane, the body is acted upon by the component of acceleration due to gravity:
$$ a = g^* = g \cdot\cos{45^{\circ}}$$
From the formula for flight range obtained in <a href="../1.3.6" target="_blank">1.3.6</a> it follows:
<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">
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<meta name="description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<meta name="description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<meta property="og:title" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<meta property="og:title" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
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<meta property="og:description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<meta property="og:description" content="A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.">
<title>A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.</title>
<title>A ball is launched along a smooth inclined plane at a speed of v. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of 45^\circ . The initial velocity of the ball forms an angle of 45^\circ with the horizontal edge of the plane.</title>
$1.3.7.$ A ball is launched along a smooth inclined plane at a speed of $v$. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of $45^\circ$ . The initial velocity of the ball forms an angle of $45^\circ$ with the horizontal edge of the plane.
$1.3.7.$ A ball is launched along a smooth inclined plane at a speed of $v$. How much horizontal distance will it travel before it rolls off the plane? The plane is inclined to the horizon at an angle of $45^\circ$ . The initial velocity of the ball forms an angle of $45^\circ$ with the horizontal edge of the plane.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $1.3.7$
For problem $1.3.7$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="drawing.png"
<img src="drawing.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
Effective acceleration of free fall ($g^*$)
Effective acceleration of free fall ($g^*$)
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
On an inclined plane, the body is acted upon by the component of acceleration due to gravity:
On an inclined plane, the body is acted upon by the component of acceleration due to gravity:
$$ a = g^* = g \cdot\cos{45^{\circ}}$$
$$ a = g^* = g \cdot\cos{45^{\circ}}$$
From the formula for flight range obtained in <a href="../1.3.6" target="_blank">1.3.6</a> it follows:
From the formula for flight range obtained in <a href="../1.3.6" target="_blank">1.3.6</a> it follows:
<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>
