Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat of m

Question

Two people, one of mass 75 kg and the other of mass 60 kg, sit in a rowboat of mass 100 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 5.0 m apart from each other, exchange seats.

(a) How far will the boat move

(b) In what direction will the boat move?

          It will move toward the initial position of the 75 kg person.

          None of these is correct.

          It will move toward the initial position of the 60 kg person.

          It will not move

Explanation / Answer

a)

m1 = mass of person 1 = 75 kg

m2 = mass of person 2 = 60 kg

m3 = mass of boat = 100 kg

let m1 sits at the left end and me at right end of the boat and lets assume that left end of the boat is at origin

x1 = position of mass m1 = 0 m

x2 = position of mass m2 = 3 m

x3 = position of center of boat where all mass of boat can be assumed = 3/2 = 1.5 m

center of mass of system is given as

x = (m1 x1 + m2 x2 + m3 x3) / (m1 + m2 + m3)

x = (75 x 0 + 60 x 3 + 100 x 1.5) / (75 + 60 + 100)

x = 330 / 235 = 1.404 m   from left end

now m1 and m2 exchange the position

x = (m1 x2 + m2 x1 + m3 x3) / (m1 + m2 + m3)

x = (75 x 3 + 60 x 0 + 100 x 1.5) / (75 + 60 + 100)

x = 1.595 m

movement of boat = 1.595 - 1.404 = 0.191 m

b)

It will move toward the initial position of the 75 kg person.so the center of mass of the system remains at the same position

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