Question

Romeo (85.0 kg) entertains Juliet (47.0 kg) by playing his guitar from the rear of their boat at rest in still water, 2.70 m away from Juliet, who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek. How far does the 83.0-kg boat move toward the shore it is facing?

Answer 1

Answer:

Δ = 0.59 m towards shore

Explanation:

Given:

m r = 85.0 kg , m j = 47.0 kg , m b = 83.0 kg , L = 2.70 m

X'cm = X cm

mj xj + mb xb + mr xr / mj + mb +mr

L (mb / 2 +mr) = mj (L/2 - Δ + L/2) + mb ( L/2 - Δ) + mr ( L/2 - Δ + L/2)

Δ (mj + mb +mr) = L (mj +mb/2 + mr) - L (mb/2 +mr)

Δ = L * mj / (mj +mb + mr)

Replacing numeric

Δ = 2.70 m * [ 47.0 kg / ( 47.0 + 83.0 + 85.0 )]

Δ = 0.59 m towards shore