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March 1, 2015

March 1, 2015

Posted by **sarsi** on Thursday, September 5, 2013 at 6:31am.

- physics -
**Graham**, Thursday, September 5, 2013 at 7:13amConserve momentum. (Initial = final)

(1) Man and boy simultaneously jump and push the boat back.

m1 = mass of man

m2 = mass of boy

v1 = velocity of man (and boy)

m3 = mass of boat

v3 =

0 = (m1+m2) v1 + m3 v3

Rearrange:

v3 = - (m1+m2) v1 / m3

= - 100 * 2 / 150

= 1.33 m/s

(2) First, the man pushes back the boat and the boy, then the boy further pushes back the boat.

Key point: When the boy jumps off at v1 _relative_ to the boat, the boat is not at rest.

m1 = mass of man

m2 = mass of boy

v1 = velocity of man

v2 = intermediate velocity of boat

m3 = mass of boat

v4 = final velocity of boat

First jump:

0 = m1 v1 + (m2+m3) v2

Second jump:

(m2+m3) v2 = m2 (v2+v1) + m3 v4

Rearrange:

v2 = - m1 v1 / (m2+m3)

v4 = v2 - (m2 v1)/ m3

Substitute first into the second

v4 = - (m1/(m2+m3)+m2/m3) v1

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