Chapter 2, Problem 73GP

To determine

The time taken by the car to pass the train and the distance travelled by the car in this time if the car and train are travelling in same direction. Also the time taken by the car to pass the train and the distance travelled by the car if the car and train are travelling in opposite directions.

Answer to Problem 73GP

The time taken by the car to pass the train if the car and train are travelling in same direction is $t=198\text{ s}$ .

The distance traveled by the car in this time if the car and train are travelling in same direction is $L=5.23\text{ km}$ .

The time taken by the car to pass the train if the car and train are travelling in opposite directions is $t=23.4\text{ s}$ .

The distance traveled by the car in this time if the car and train are travelling in opposite directions is $L=0.62\text{ km}$ .

Explanation of Solution

Given:

The speed of the car is $v_{\text{car}}=95\text{km}/\text{h}$ .

The length of the train is $d=1.10\text{ km}$ .

The speed of the train is $v_{\text{train}}=75\text{km}/\text{h}$ .

Formula used:

The expression for relative speed is,

  $v=v_{\text{car}}-v_{\text{train}}$

Here, $v_{\text{car}}$ is the speed of the car and $v_{\text{train}}$ is the speed of the train.

The expression for the time is,

  $t=\frac{d}{v}$

Here, d is the distance travelled and v is the relative speed.

The expression for the distance travelled is,

  $L=v_{\text{car}}t$

Here, $v_{\text{car}}$ is the speed of the car and t is the time.

Calculation:

Consider the car and train is travelling in same direction.

The relative speed is,

  $\begin{array}{c}v=v_{\text{car}}-v_{\text{train}}\\ =\left(95\text{km}/\text{h}\right)-\left(75\text{km}/\text{h}\right)\\ =20\text{km}/\text{h}\end{array}$

The time taken by the car to pass the train is,

  $\begin{array}{l}t=\frac{d}{v}\\ t=\frac{1.10\text{ km}}{20\text{km}/\text{h}}\\ t=0.055\text{ h}\times \frac{60\text{ min}}{1\text{ hr}}\times \frac{60\text{ s}}{1\text{ min}}\\ t=198\text{ s}\end{array}$

The distance travelled by the car, if both are travelling in same direction, is

  $\begin{array}{c}L=v_{\text{car}}t\\ L=\left(\text{95 }\text{km}/\text{h}\right)\times \left(0.055\text{ h}\right)\\ L=5.23\text{ km}\end{array}$

The relative speed , when both vehicles are travelling in opposite directions, is

  $\begin{array}{c}v=v_{\text{car}}-v_{\text{train}}\\ =\left(95\text{km}/\text{h}\right)-\left(-75\text{km}/\text{h}\right)\\ =170\text{km}/\text{h}\end{array}$

The time taken by the car to pass the train, if both are travelling in opposite direction, is

  $\begin{array}{l}t=\frac{d}{v}\\ t=\frac{1.10\text{ km}}{170\text{km}/\text{h}}\\ t=0.0065\text{ h}\times \frac{60\text{ min}}{1\text{ hr}}\times \frac{60\text{ s}}{1\text{ min}}\\ t=23.4\text{ s}\end{array}$

The distance travelled by the car if the car and train is travelling in opposite direction is,

  $\begin{array}{c}L=v_{\text{car}}t\\ L=\left(\text{95 }\text{km}/\text{h}\right)\times \left(0.0065\text{ h}\right)\\ L=0.62\text{ km}\end{array}$

Conclusion:

Thus, the time taken by the car to pass the train if the car and train are travelling in same direction is $t=198\text{ s}$ .

Thus, the distance travelled by the car in this time if the car and train are travelling in same direction is $L=5.23\text{ km}$ .

Thus, the time taken by the car to pass the train if the car and train are travelling in opposite directions is $t=23.4\text{ s}$ .

Thus, the distance traveled by the car in this time if the car and train are travelling in opposite directions is $L=0.62\text{ km}$ .