Chapter 2.4, Problem 36PP

To determine

To Find: The final position of each ship if both the ships start from point B and travel towards west.

Answer to Problem 36PP

The position of first and second ship relative to position A is $52\mathrm{km}$ and $40\mathrm{km}$ towards west, respectively.

Explanation of Solution

Given:

The average velocity of first ship is $35\text{km/h}$ , while that of second ship is $26\text{}\mathrm{km}/h$ .

The time taken by first ship is $2.2\text{ h}$ , while that taken by second ship is $2.5\text{ h}$ .

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 first ship in $2.2\text{h}$ with respect to the point Bis,

  ${\overline{v}}_{\text{1}}=\frac{x_1-x_B}{t_1-t_B}$

  ${\overline{v}}_{\text{1}}=35\text{km/h}$

  $t_1-t_B=2.2\text{h}$

  $\begin{array}{c}{x}_{1B}=x_1-x_B\\ =35\times 2.2\\ =77\mathrm{km}\text{ towards West}\end{array}$

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

  $\begin{array}{c}{x}_{1A}=x_{1B}-x_{AB}\\ =\left(77-25\right)\mathrm{km}\\ =52\mathrm{km}\text{ with respect to }A\end{array}$

Similarly, the distance travelled by the second ship in $2.5\text{h}$ with respect to the point Bis,

  ${\overline{v}}_{\text{2}}=\frac{x_2-x_B}{t_2-t_B}$

  ${\overline{v}}_{\text{2}}=26\text{km/h}$

  $t_2-t_B=2.5\text{h}$

  $\begin{array}{c}{x}_{2B}=x_2-x_B\\ =26\times 2.5\\ =65\mathrm{km}\text{ towards West}\end{array}$

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

  $\begin{array}{c}{x}_{2A}=x_{2B}-x_{AB}\\ =\left(65-25\right)\mathrm{km}\\ =40\mathrm{km}\text{ with respect to }A\end{array}$

Conclusion:

Thus, the first ship’s position after 2.2h, relative to the starting point A is $52\mathrm{km}$ towards west while that of the second position after 2.5h relative to the starting point A is $40\mathrm{km}$ towards west.