# Relative velocity and momentum

1. Dec 1, 2008

### Maiia

1. The problem statement, all variables and given/known data
Tｏｎｙ　（ｏｆ　ｍａｓｓ　５０ｋｇ）ｃｏａｓｔｓ　ｏｎ　ｈｉｓ　ｂｉｃｙｃｌｅ　（ｏｆ　ｍａｓｓ　５　ｋｇ）ａｔ　ａ　ｃｏｎｓｔａｎｔ　ｓｐｅｅｄ　ｏｆ　６ｍ／ｓ，　ｃａｒｒｙｉｎｇ　ａ　１２　ｋｇ　ｐａｃｋ．　Ｔｏｎｙ　ｔｈｒｏｗｓ　ｈｉｓ　ｐａｃｋ　ｆｏｒｗａｒｄ，　ｉｎ　ｔｈｅ　ｄｉｒｅｃｔｉｏｎ　ｏｆ　ｈｉｓ　ｍｏｔｉｏｎ，　ａｔ　２ｍ／ｓ　ｒｅｌａｔｉｖｅ　ｔｏ　ｔｈｅ　ｓｐｅｅｄ　ｏｆ　ｔｈｅ　ｂｉｃｙｃｌｅ　ｊｕｓｔ　ｂｅｆｏｒｅ　ｔｈｅ　ｔｈｒｏｗ．　Ｗｈａｔ　ｉｓ　ｔｈｅ　ｉｎｉｔｉａｌ　ｍｏｍｅｎｔｕｍ　ｏｆ　ｔｈｅ　ｓｙｓｔｅｍ　（Ｔｏｎｙ，　ｔｈｅ　ｂｉｃｙｃｌｅ，　ａｎｄ　ｔｈｅ　ｐａｃｋ）？
Ａｎｓｗｅｒ　ｉｎ　ｕｎｉｔｓ　ｏｆ　ｋｇｍ／ｓ．

Ｄｏｅｓ　ｒｅｌａｔｉｖｅ　ｖｅｌｏｃｉｔｙ　ｈｅｒｅ　ｍｅａｎ　ｔｈａｔ　ｔｈｅ　ｐａｃｋ　ｉｓ　ａｃｔｕａｌｌｙ　ｍｏｖｉｎｇ　ａｔ　８ｍ／ｓ？Ｉ＇ｍ　ａ　ｌｉｔｔｌｅ　ｃｏｎｆｕｓｅｄ　ａｓ　ｔｏ　ｗｈａｔ　ｒｅｌａｔｉｖｅ　ｖｅｌｏｃｉｔｙ　ｉｓ．　To get initial momentum, I　ｗｏｕｌｄ　ｊｕｓｔ　ａｄｄ　ａｌｌ　ｔｈｅｉｒ　ｍｏｍｅｎｔｕｍｓ　ｔｏｇｅｔｈｅｒ，　ｒｉｇｈｔ？Ｂｅｃａｕｓｅ　ｔｈｅｙ　ｈａｖｅ　ｄｉｆｆｅｒｅｎｔ　ｓｐｅｅｄｓ？　Ｂｅｃａｕｓｅ　Ｉ don't think Ｉ would be able to add their masses together and multiply by the velocity.

2. Dec 1, 2008

### turin

Yes, relative to the speed of the bike just means that you should imagine that the bike is at rest and the earth is moving 6 m/s backward. So, yes, the pack is moving at 8 m/s relative to the earth. However, are you sure this is relevant to the question that the problem asks?

3. Dec 1, 2008

### Maiia

hmm i guess not b/c the pack should be moving at the same speed as the boy and the bike..but it would be if i were asked to find the momentum of the system after the pack was thrown i think..

4. Dec 1, 2008

Careful ...