# How do I find the speed of an ice chunk over an ice rink when a person walks atop?

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?.

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?.

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).

• 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. – Chris Steinbeck Bell Dec 8 '19 at 20:51
• Momentum of person + momentum of ice chunk = 0 – tomi Dec 8 '19 at 20:56
• Do you know how to find the momentum of an object if you know its mass and its velocity? – tomi Dec 8 '19 at 20:57
• 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?. – Chris Steinbeck Bell Dec 8 '19 at 20:59
• Use $(3.7-v)$ for the person and $-v$ for the ice chunk. – tomi Dec 8 '19 at 21:00