Question #283280

A 4.5 kg dog stands on an 18 kg flatboat at dis-

tance D ! 6.1 m from the shore. It

walks 2.4 m along the boat toward

shore and then stops. Assuming no

friction between the boat and the wa-

ter, find how far the dog is then from

the shore.


1
Expert's answer
2021-12-30T11:54:15-0500

Since the momentum is conserved:


0=mbvbmdvd, v=dt, 0=mbdbtmdddt, 0=mbdbmddd.0=m_bv_b-m_dv_d,\\\space\\ v=\dfrac dt,\\\space\\ 0=m_b\dfrac{d_b}{t}-m_d\dfrac{d_d}{t},\\\space\\ 0=m_bd_b-m_dd_d.


The sum of the displacements is 2.4 m:


db+dd=2.4 m.d_b+d_d=2.4 \text{ m.}


Solve the system of equations:


dd=1.92 m,dd=0.48 m.d_d=1.92\text{ m},\\ d_d=0.48\text{ m}.

The displacement of dog is 1.92 m forward, the distance to the shore is 6.1-1.92=4.18 m.


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