Chapter 2.4, Problem 42SSC

To determine

To Calculate: The distance covered by the cars from the point B and the position of cars relative to A.

Answer to Problem 42SSC

The distance covered by the red car is $8\mathrm{km}$ to east from point B and the distance covered by the blue car is $12\mathrm{km}$ to west from the point B.

The position of the red car relative to point A is $14\mathrm{km}$ and the position of the blue car relative to point B is $6\mathrm{km}$ .

Explanation of Solution

Given:

The red car travels for a time, $t_1=0.25\mathrm{h}$

The velocity of the red car to the east, $v_1=32\mathrm{km}/h$

The blue car travels for a time, $t_2=0.25h$

The velocity of the blue car towards the west, $v_2=48\mathrm{km}/h$

The distance between the points A and B is $d_0{}_{ }=6\mathrm{km}$ .

The distance between the points B and C is $d_1=8\mathrm{km}$ .

The distance between the points B and D is $d_2=12\mathrm{km}$ .

Let $D_{CA}$ is the position of the car relative to point A

  $D_{DA}$ is the position of the car relative to point A

Let $d_1$ and $d_2$ are the distances covered by the red car and blue car respectively from the point B.

Formula used:

The distance travelled $d$ in terms of velocity $v$ and time $t$ is

  $d=v\times t$

Calculation:

The distance travelled by the red car from the point B is

  $\begin{array}{l}{d}_{\text{1}}{\text{= v}}_{\text{1}}{t}_{\text{1}}\\ d_{\text{1}}\text{=}\left(\text{32 km/h}\right)\left(\text{0}\text{.25 h}\right)\\ d_{\text{1}}\text{= 8 km}\end{array}$

The distance travelled by the blue car from the point B is

  $\begin{array}{l}{d}_2{\text{= v}}_2{t}_2\\ d_2\text{=}\left(\text{48 km/h}\right)\left(\text{0}\text{.25 h}\right)\\ d_{\text{1}}\text{= 12 km}\end{array}$

The position of the red car at C relative to A is the distance between the point A and C

  $\begin{array}{l}{D}_{CA}=d_1+d_0\\ D_{CA}=8\mathrm{km}+6\mathrm{km}\\ D_{CA}=14\mathrm{km}\end{array}$

The position of the blue car at D relative to A is the distance between the point A and D

  $\begin{array}{l}{D}_{DA}=d_2-d_0\\ D_{DA}=12\mathrm{km}-6\mathrm{km}\\ D_{DA}=6\mathrm{km}\end{array}$

Conclusion:

The distance covered by the red car is $8\mathrm{km}$ to east from point B and the distance covered by the blue car is $12\mathrm{km}$ to west from the point B.

The position of the red car relative to point A is $14\mathrm{km}$ and the position of the blue car relative to point B is $6\mathrm{km}$ .