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The problem is as follows:

The figure from below shows a person whose mass is $60\,kg$ is standing over a chunk of ice whose mass is $125\,kg$ which was initially at rest. The person runs across the ice chunk with a speed of $3.7\,\frac{m}{s}$ with respect of the ice chunk. What will be the speed of the ice chunk with respect of the ice rink?.

Sketch of the problem

The alternatives given in my book are as follows:

$\begin{array}{ll} 1.&0.6\,\frac{m}{s}\\ 2.&3.6\,\frac{m}{s}\\ 3.&24\,\frac{m}{s}\\ 4.&1.2\,\frac{m}{s}\\ 5.&24\,\frac{m}{s}\\ \end{array}$

I'm stuck with this problem as I'm not sure how to proceed with the appropiate calculation for the speed of the ice chunk. Should I consider that there is a conservation of momentum?. How exactly should I put the equation for the momentum?. Can someone help me with this?. I would really like to show something but in this problem I'm stuck at the very beginning.

I believe that for this problem I have to consider the momentum at the beginning is the same at the end but how can I put these into math?.

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Conservation of linear momentum.

Initial momentum is zero.

Let the velocity of the ice chunk relative to the ground be $-v$ (it has to go backwards).

The velocity of the person is $3.7$ m/s relative to the ice chunk, but $3.7-v$ m/s relative to the ground. That is very important.

Write down an expression for the total momentum of person and ice chunk. Set it equal to zero. Solve to find $v$.

In response to a comment... If you want to assume that the velocity of the ice chunk is $v$ m/s forwards, then you would have to make the person's velocity be $3.7+v$ m/s. Say total momentum is zero and solve. You will discover that $v$ is a negative value (going in the opposite direction to what you thought).

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  • $\begingroup$ Perhaps can you show the equations so I can follow what you meant?. I don't know how to find the total momentum for the person and the ice chunk. $\endgroup$ – Chris Steinbeck Bell Dec 8 '19 at 20:51
  • $\begingroup$ Momentum of person + momentum of ice chunk = 0 $\endgroup$ – tomi Dec 8 '19 at 20:56
  • $\begingroup$ Do you know how to find the momentum of an object if you know its mass and its velocity? $\endgroup$ – tomi Dec 8 '19 at 20:57
  • $\begingroup$ I do know $p=mv$ But I'm confused with the relative velocity. Which speed should I use for the momentum of the person and the momentum of the ice chunk?. $\endgroup$ – Chris Steinbeck Bell Dec 8 '19 at 20:59
  • $\begingroup$ Use $(3.7-v)$ for the person and $-v$ for the ice chunk. $\endgroup$ – tomi Dec 8 '19 at 21:00

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