Chapter 3, Problem 59GP

To determine

The time taken by the car to pass the train, distance covered by the car in this time and time and distance for the car for opposite to the train.

Answer to Problem 59GP

The time taken by the train to cross the train for same direction is $0.05\text{h}$ , the distance covered by the train in the time to cross the train in same direction is $4.75\text{km}$ , the time taken by the train to cross the train for opposite direction is $0.0058\text{h}$ and the distance covered by the train in the time to cross the train in opposite direction is $0.551\text{km}$ .

Explanation of Solution

Given info:

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

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

The length of the train is, $l=1\text{km}$ .

Formula Used:

The expression to calculate the time taken by the car to cross the train in the same direction of train is,

  $t_s=\frac{l}{v_c-v_t}\mathrm{......}\left(1\right)$

The expression to calculate the distance covered by the car in passing the train for same direction is,

  $d_s=v_c{t}_s\mathrm{......}\left(2\right)$

The expression to calculate the time taken by the car to cross the train in the opposite direction of train is,

  $t_o=\frac{l}{v_c+v_t}\mathrm{......}\left(3\right)$

The expression to calculate the distance covered by the car in passing the train for opposite direction is,

  $d_o=v_c{t}_o\mathrm{......}\left(4\right)$

Calculation:

Substitute al the values in the expression (1).

  $\begin{array}{c}{t}_s=\frac{1\text{km}}{95\text{km/h}-75\text{km/h}}\\ =0.05\text{h}\end{array}$

Substitute al the values in the expression (2).

  $\begin{array}{c}{d}_s=\left(95\text{km}/\text{h}\right)\left(0.05\text{h}\right)\\ =4.75\text{km}\end{array}$

Substitute al the values in the expression (3).

  $\begin{array}{c}{t}_o=\frac{1\text{km}}{95\text{km/h}+75\text{km/h}}\\ =0.0058\text{h}\end{array}$

Substitute al the values in the expression (4).

  $\begin{array}{c}{d}_o=\left(95\text{km}/\text{h}\right)\left(0.0058\text{h}\right)\\ =0.551\text{km}\end{array}$

Conclusion:

Thus, the time taken by the train to cross the train for same direction is $0.05\text{h}$ , the distance covered by the train in the time to cross the train in same direction is $4.75\text{km}$ , the time taken by the train to cross the train for opposite direction is $0.0058\text{h}$ and the distance covered by the train in the time to cross the train in opposite direction is $0.551\text{km}$ .