Chapter 2.4, Problem 35PP

To determine

To Find: The ship’s position if the ship starts at point B and travels towards west to point D.

Answer to Problem 35PP

  $17\mathrm{km}$

Explanation of Solution

Given:

The average velocity of the ship is $35\text{km/h}$ .

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

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, the distance travelled by the ship in $1.2\text{h}$ with respect to the point Bis:

  ${\overline{v}}_{\text{constant}}=\frac{x_D-x_B}{t_D-t_B}$

Use:

  ${\overline{v}}_{\text{constant}}=35\text{km/h}$

  $t_D-t_B=1.2\text{h}$

  $\begin{array}{c}{x}_{DB}=x_D-x_B\\ =35\times 1.2\\ =42\mathrm{km}\text{ towards West}\end{array}$

Hence, the distance travelled by the ship with respect to the initial position A will be,

  $\begin{array}{c}{x}_{DA}=x_{DB}-x_{AB}\\ =\left(42-25\right)\mathrm{km}\\ =17\mathrm{km}\text{ with respect to }A\end{array}$

Conclusion:

Thus, the ship’s position after 1.5h, relative to the starting point A is $17\mathrm{km}$ towards west.