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If you throw a ball horizontally while standing on roller skates, you roll backward with a momentum that matches that of the ball. Will you roll backward if you go through the motions of throwing the ball, but instead hold on to it? Explain. Assuming you've answered them in terms of momentum conservation, answer them also in terms of Newton's third law (or vice versa, if you answered already in terms of Newton's third law)

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Answer:

No, in that case we will not roll backwards.

Explanation:

When we throw a ball forward then as we know by momentum conservation we know that

[tex]P_i = P_f[/tex]

as we know that the boy + ball is at rest then initial momentum is zero

so we can say

[tex]0 = m_{boy}v_{boy} + m_{ball}v_{ball}[/tex]

so we can say

[tex]v_{boy} = - \frac{m_{ball}v_{ball}}{m_{boy}}[/tex]

now let say the boy go through the motion of throwing the ball but ball is still in his hand then we can say that

[tex]v_{ball} = v_{boy}[/tex]

since they are initially at rest so final momentum of both must be zero

so final speed of both must be zero

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