document.write( "Question 1189951: Hello, these are physics problems. Help please
\n" ); document.write( "1. A 0.22 kg red striped pool ball is moving at 3.0 m/s North and it collides with a white cue ball that is 0.25 kg and it is moving at 1.0 m/s South. After the collision, the red striped ball continues at 2.5 m/s North. What is the velocity of the white cue ball?
\n" ); document.write( "2. Two skaters are skating towards each other. The 75.0 kg man is moving at 2.0 m/s to the right, and he picks up the 40.0 kg woman skater who is moving at - 1.5 m/s to the left. What speed and direction do they move off together (assuming no friction on the ice)? \n" ); document.write( "

Algebra.Com's Answer #821475 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "1. A 0.22 kg red striped pool ball is moving at 3.0 m/s North and it collides with a white cue ball
\n" ); document.write( " that is 0.25 kg and it is moving at 1.0 m/s South. After the collision, the red striped ball continues
\n" ); document.write( " at 2.5 m/s North. What is the velocity of the white cue ball?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. Two skaters are skating towards each other. The 75.0 kg man is moving at 2.0 m/s to the right,
\n" ); document.write( " and he picks up the 40.0 kg woman skater who is moving at - 1.5 m/s to the left.
\n" ); document.write( " What speed and direction do they move off together (assuming no friction on the ice)?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            The solution by @mananth to problem 1 is ABSOLUTELY WRONG. So, I came to bring correct calculations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            Next, the problem itself is posed INCORRECTLY, as I will explain it in my post-solution note.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                        Problem 1\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Since two balls move in opposite directions, vectors along North axis contribute with the \" + \" sign,\r\n" );
document.write( "while vectors along South axis contribute with the \" - \" sign \".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The momentum of the red   ball before collision is   =  0.22*3   =  0.66 (kg*m)/s.\r\n" );
document.write( "\r\n" );
document.write( "The momentum of the white ball before collision is   = -0.25*1   = -0.25 (kg*m)/s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The momentum of the red   ball after collision is     =  0.22*2.5 = 0.55 (kg*m)/s.\r\n" );
document.write( "\r\n" );
document.write( "The momentum conservation law states that the total moment after collision is the same as before collision\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     +  =  + \r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "    0.66 - 0.25 = 0.55 + ,   in (kg*m)/s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this equation, you find the momentum of the white ball after collision  \r\n" );
document.write( "\r\n" );
document.write( "     = 0.66 - 0.25 - 0.55 = -0.14  (kg*m)/s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As the last step, you find the velocity of the white ball after collision by dividing its momentum by its mass\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    velocity of the white ball after collision =  = -0.056 m/s.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The sign \"-\" tells that white ball moves south after collision.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the formal calculations are completed.\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But look what we get.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The red ball initially moved North and continues moving North after collision.\r
\n" ); document.write( "\n" ); document.write( "The white ball initially moved South and continues moving South after collision.\r
\n" ); document.write( "\n" ); document.write( "It means, physically, then the balls \" penetrated \" through each other,
\n" ); document.write( "which physically may not happen with real balls (no one physical experiment, so far, showed similar phenomenon).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Therefore, I think that the problem is posed physically INCORRECTLY.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "No one real physical experiment may produce such a combination of input values as presented in your post.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem as posed, with provided input data is a FAKE.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===========\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The solution by @mananth is wrong, since he uses incorrect expressions for the momentum,\r
\n" ); document.write( "\n" ); document.write( "placing incorrect signs there.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );