Question

A 107 kg boat that is 7 m in length is initially 7.3 m from the pier. A 53 kg child stands at the end of the boat closest to the pier. The child then notices a turtle on a rock at the far end of the boat and proceeds to walk to the far end of the boat to observe the turtle. 7.3 m 7 m How far is the child from the pier when she reaches the far end of the boat

Answer 1

11.98 m

Step-by-step explanation:

Given that:

mass of the child
`m_c` = 53 kg

mass of the boat
`m_b` = 107 kg

`\text{length of the boat L = 7 m}`

the distance of the boat from pies l = 7.3 m

initial momentum
`P_i = 0`

Final momentum
`P_f = mc (L)/(f)- (m_c +m_b) (x)/(l)`

where;

x = distance moved by boat towards left

t = time taken for the child to travel to the far end of the boat

`P_i =P_f`

∴

`m_c (L)/(t)=(m_c +m_b) (x)/(t)`

Then;

`x = (m_cL)/(m_c+m_b)`

`x = (53 * 7)/(53+107)`

x = 2.32 m

The distance of the child from the pier is:

d = L +(l - x)

d = 7 m + ( 7.3 m - 2.32 m)

d = 7 m + 4.98 m

d = 11.98 m