Question

A dog, with a mass of 10.0 kg, is standing on a flatboat so that he is 22.5 m from the shore. He walks 7.8 m on the boat toward the shore and then stops. The boat has a mass of 46.0 kg. Assuming there is no friction between the boat and the water, how far is the dog from the shore now?

Answer 1

Answer:16.096

Step-by-step explanation:

Given

mass of dog
`\left ( m_d\right )=10kg`

mass of boat
`\left ( m_b\right )=46kg`

distance moved by dog relative to ground=
`x_d`

distance moved by boat relative to ground=
`x_b`

Distance moved by dog relative to boat=7.8m

There no net force on the system therefore centre of mass of system remains at its position

0=
`m_d* x_d+m_b\dot x_b`

0=
`10* x_d+46\dot x_b`

`x_d=-4.6x_b`

i.e. boat will move opposite to the direction of dog

Now

`|x_d|+|x_b|=7.8`

substituting
`x_d`value

`5.6|x_b|=7.8`

`|x_b|=1.392m`

`|x_d|=6.4032m`

now the dog is 22.5-6.403=16.096m from shore