Chapter 2.4, Problem 33PP

To determine

To Find: The ship’s position when it reaches point C, relative to the starting point A.

Answer to Problem 33PP

  $88\mathrm{km}$

Explanation of Solution

Given:

The ship is sailing at a constant velocity, $v=42\text{km/h}$ .

The distance between points A and B,is 25 km.

And, the ship sails from point B to point C in 1.5h.

Formula used:

The average velocity of a particle is given by

  $\overline{v}=\frac{\Delta d}{\Delta t}=\frac{d_{final}-d_{initial}}{t_{final}-t_{initial}}$

Calculation:

Using the above formula of average velocity between points B and C,

  ${\overline{v}}_{\text{constant}}=\frac{x_C-x_B}{t_C-t_B}$

Using,

  ${\overline{v}}_{\text{constant}}=42\text{}\text{km/h}$

  $t_C-t_B=1.5\text{h}$

  $\begin{array}{c}{x}_{CB}=x_C-x_B\\ =42\times 1.5\\ =63\mathrm{km}\end{array}$

Hence, the position of point C with respect to the initial position A is:

  $\begin{array}{c}{x}_{CA}=25+x_{CB}\\ =\left(25+63\right)\mathrm{km}\\ =88\mathrm{km}\end{array}$

Conclusion:

Thus, the ship’s position when it reaches point C, relative to the starting point A is $88\mathrm{km}.$