document.write( "Question 1181710: A rocket is being launched vertically over a point 𝐴 on the ground with
\n" ); document.write( "a velocity of 550 𝑚𝑖Τℎ𝑟. Twenty five miles away from point 𝐴 on the
\n" ); document.write( "ground, there is a photographer video-taping the launch. At what rate
\n" ); document.write( "is the angle of elevation of the camera changing when the rocket
\n" ); document.write( "achieves an altitude of 25 miles? \n" ); document.write( "

Algebra.Com's Answer #814128 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

 \r\n" );
document.write( "You don't need to clarify anything. This is an ordinary related rates problem\r\n" );
document.write( "from calculus.  \r\n" );
document.write( "

\n" ); document.write( "A rocket is being launched vertically over a point 𝐴 on the ground with
\n" ); document.write( "a velocity of 550 𝑚𝑖Τℎ𝑟. Twenty five miles away from point 𝐴 on the
\n" ); document.write( "ground, there is a photographer video-taping the launch. At what rate
\n" ); document.write( "is the angle of elevation of the camera changing when the rocket
\n" ); document.write( "achieves an altitude of 25 miles?
\n" ); document.write( "

  \r\n" );
document.write( "h = the height of the rocket\r\n" );
document.write( "θ = the angle of elevation of the camera.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Take derivatives of both sides with respect to time t:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " the upward speed of the rocket, which is given as 550 miles/hour\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 25\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Change  to \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by :\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next we calculate the value of  when\r\n" );
document.write( "the rocket is 25 miles high.\r\n" );
document.write( "\r\n" );
document.write( "The figure we are \"freezing\" the rocket at looks like this, so that's when\r\n" );
document.write( ":\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since , we substitute:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " radians/hour\r\n" );
document.write( "\r\n" );
document.write( "That's about 15.6 radians per hr.\r\n" );
document.write( "\r\n" );
document.write( "That's about 14.8 degrees per minute.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );