<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta property="og:title" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<title>At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.</title>
$1.3.9.$ At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration $a$? The distance from the gun to the rocket launch site is $L$, the gun fires at an angle of $45^\circ$ to the horizon.
</p>
<h3>Solution</h3>
<p>
Let's use the formula for the $x$ and $y$ coordinates obtained in <a href="../1.3.6" target="_blank">1.3.6</a>:
$$ y(t) = \frac{1}{\sqrt{2}}vt - \frac{gt^2}{2}$$
$$ x(t) = \frac{1}{\sqrt{2}}vt $$
In this case, the equation describing the rocket’s motion is:
<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="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta name="description" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta property="og:title" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta property="og:title" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<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="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<meta property="og:description" content="At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.">
<title>At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.</title>
<title>At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration a? The distance from the gun to the rocket launch site is L, the gun fires at an angle of 45^\circ to the horizon.</title>
$1.3.9.$ At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration $a$? The distance from the gun to the rocket launch site is $L$, the gun fires at an angle of $45^\circ$ to the horizon.
$1.3.9.$ At what speed should a projectile fly out of a cannon at the moment of rocket launch in order to hit a rocket starting vertically with acceleration $a$? The distance from the gun to the rocket launch site is $L$, the gun fires at an angle of $45^\circ$ to the horizon.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
Let's use the formula for the $x$ and $y$ coordinates obtained in <a href="../1.3.6" target="_blank">1.3.6</a>:
Let's use the formula for the $x$ and $y$ coordinates obtained in <a href="../1.3.6" target="_blank">1.3.6</a>:
$$ y(t) = \frac{1}{\sqrt{2}}vt - \frac{gt^2}{2}$$
$$ y(t) = \frac{1}{\sqrt{2}}vt - \frac{gt^2}{2}$$
$$ x(t) = \frac{1}{\sqrt{2}}vt $$
$$ x(t) = \frac{1}{\sqrt{2}}vt $$
In this case, the equation describing the rocket’s motion is:
In this case, the equation describing the rocket’s motion is:
<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>
