Question

A boy and a girl are resting on separate rafts 14 m apart in calm water when the girl notices a small beach toy floating midway between the rafts. The girl and her raft have three times the inertia of the boy and his raft. The rafts are connected by a rope 16 m long, so she decides to pull on the rope, drawing the rafts together until she can reach the toy. How much distance is there between the two rafts when the first one reaches the toy?

Answer 1

To solve this problem we will apply the concepts related to the kinematic equations of linear motion. Where speed is described as the distance traveled in a given time, and the successive equivalences that can be made under that equation.

The distance traveled by the girl with in the given time is

$d_g = v_g t$

The distance covered by the boy with in the given time is

$d_b = v_b t$

Since the boy will travels with twice the speed of the girl

$d_b = v_b t$

$d_b = 2v_g t$

$d_b = 2d_g$

Half way between the two rafts at the beginnings is

$\frac{14m}{2} = 7m$

$7m = 2d_g$

$d_g = 3.5m$

The final distance between the two rafts at the instant the boy reached the central point of the line joining between them is

$\Delta d = d_b-d_g$

$\Delta d = 7m-3.5m$

$\Delta d = 10.5m$

Therefore the distance that there is between the two rafts when the first one reaches the toy is 10.5m