• A $50$ kg student in a $10$ kg boat is trying to rescue me with a rope. I am a $100$ kg professor in a $20$ kg boat. Thestudent tosses me a rope, and I grab hold of the end. I hold my end tight, while the student $($doing all the work$)$pulls the rope into their boat at a speed of $3$ meters per second. Assume we were originally $30$ meters apart, thetemperature is $5$ degree centigrade, the sky is clear blue with a bright shinning sun, and there is a black water chicken in the lake nearby watching. Everyone is originally at rest, including the bird.

  $($a$)$ What is the speed of the students relative to the water while they are pulling the rope?

  $($b$)$ How far do I move before hitting the student$’$s boat?

  $($c$)$ What is the ratio of the force the student puts on the rope to the force that I put on the rope?