<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<meta property="og:title" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
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@@ -14,9 +14,9 @@
<meta property="og:description" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<title>a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?</title>
$1.4.5.$ a. Due to air resistance, raindrops fall at a constant velocity $v$ perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of $u$ so that drops do not fall on its walls?
</p><p>
b. At a wind speed of $10$$\frac{m}{s}$, raindrops fall at an angle of $30^\circ$ to the vertical. At what wind speed will the drops fall at an angle of $45^\circ$?
a) To prevent raindrops from hitting the walls of the bucket, their relative velocity must be parallel to the walls of the bucket.
</p>
<p >
In the inertial reference frame associated with raindrops, the angle $\alpha$ between the relative velocity and the horizontal is defined as
</p>
<p class="exp">
$$\tan\varphi = u/v \; (1)$$
</p>
<p >
The walls of the bucket must be at the same angle.
</p>
<p >
b) Considering the relationship of the angle with the vertical and horizontal $\beta = 90^{\circ} - \alpha$. We substitute numerical data into $(1)$ and solve the system:
</p>
<p class="exp">
$$\left\{\begin{matrix}
10 \cdot\tan 60^{\circ} = u\\
v \cdot\tan 45^{\circ} = u
\end{matrix}\right.$$
</p>
</p>
<h4>Answer</h4>
<p>
<p>
$a.$ The bucket should be tilted in the direction of the platform's movement at an angle $\varphi$ to the vertical: $\tan\varphi = u/v.$
<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. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<meta name="description" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<meta property="og:title" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<meta property="og:title" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<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. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<meta property="og:description" content="a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?">
<title>a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?</title>
<title>a. Due to air resistance, raindrops fall at a constant velocity v perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of u so that drops do not fall on its walls? b. At a wind speed of 10 \frac{m}{s}, raindrops fall at an angle of 30^\circ to the vertical. At what wind speed will the drops fall at an angle of 45^\circ?</title>
$1.4.5.$ a. Due to air resistance, raindrops fall at a constant velocity $v$ perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of $u$ so that drops do not fall on its walls?
$1.4.5.$ a. Due to air resistance, raindrops fall at a constant velocity $v$ perpendicular to the ground surface. How is it necessary to position a cylindrical bucket on a platform moving at a speed of $u$ so that drops do not fall on its walls?
</p><p>
</p><p>
b. At a wind speed of $10$$\frac{m}{s}$, raindrops fall at an angle of $30^\circ$ to the vertical. At what wind speed will the drops fall at an angle of $45^\circ$?
b. At a wind speed of $10$$\frac{m}{s}$, raindrops fall at an angle of $30^\circ$ to the vertical. At what wind speed will the drops fall at an angle of $45^\circ$?
a) To prevent raindrops from hitting the walls of the bucket, their relative velocity must be parallel to the walls of the bucket.
a) To prevent raindrops from hitting the walls of the bucket, their relative velocity must be parallel to the walls of the bucket.
</p>
</p>
<p >
<p >
In the inertial reference frame associated with raindrops, the angle $\alpha$ between the relative velocity and the horizontal is defined as
In the inertial reference frame associated with raindrops, the angle $\alpha$ between the relative velocity and the horizontal is defined as
</p>
</p>
<p class="exp">
<p class="exp">
$$\tan\varphi = u/v \; (1)$$
$$\tan\varphi = u/v \; (1)$$
</p>
</p>
<p >
<p >
The walls of the bucket must be at the same angle.
The walls of the bucket must be at the same angle.
</p>
</p>
<p >
<p >
b) Considering the relationship of the angle with the vertical and horizontal $\beta = 90^{\circ} - \alpha$. We substitute numerical data into $(1)$ and solve the system:
b) Considering the relationship of the angle with the vertical and horizontal $\beta = 90^{\circ} - \alpha$. We substitute numerical data into $(1)$ and solve the system:
</p>
</p>
<p class="exp">
<p class="exp">
$$\left\{\begin{matrix}
$$\left\{\begin{matrix}
10 \cdot\tan 60^{\circ} = u\\
10 \cdot\tan 60^{\circ} = u\\
v \cdot\tan 45^{\circ} = u
v \cdot\tan 45^{\circ} = u
\end{matrix}\right.$$
\end{matrix}\right.$$
</p>
</p>
</p>
</p>
<h4>Answer</h4>
<h4>Answer</h4>
<p>
<p>
<p>
<p>
$a.$ The bucket should be tilted in the direction of the platform's movement at an angle $\varphi$ to the vertical: $\tan\varphi = u/v.$
$a.$ The bucket should be tilted in the direction of the platform's movement at an angle $\varphi$ to the vertical: $\tan\varphi = u/v.$
<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>
