Model 4 Train Vs Pole/Signal Post/Man Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Speed of train A

= $150/30$ = 5 m/sec.

Speed of train B = x m/sec.

Relative speed = (5+x) m/sec.

Length of both trains

= Relative speed × Time

300 = (5 + x) × 10

5 + x = $300/10$ = 30

x = 30 - 5 = 25 m/sec.

= $({25 × 18}/5)$ kmph. = 90 kmph.

Answer: (a)

Speed of train = 120 kmph.

= $({120 × 5}/18)$ m./sec. = $100/3$ m./sec.

Required time = $\text"Length of train"/ \text"Speed of train"$

= $(100/{100/3})$ seconds

= $(100/100 × 3)$ seconds = 3 seconds

Answer: (b)

When a train crosses a pole it travels a distance equal to its length.

Speed of train

= $240/16$ = 15 m./sec.

= $(15 × 18/5)$ kmph = 54 kmph.

Answer: (a)

Using Rule 1,

Speed of train = 36 kmph

= $({36 × 5}/18)$ m/sec = 10 m/sec.

Length of train = Speed × time

= 10 × 25 = 250 metre

Answer: (b)

Let the speed of train be x kmph

and its length be y km.

When the train crosses a man, it covers its own length

According to he question,

$y/{(x - 3) × 5/18}$ = 10

18y = 10 × 5(x –3)

18y = 50x –150 ..... (i)

and, $y/{(x - 5) × 5/18}$ = 11

18y = 55(x–5)

18y = 55x –275 .... (ii)

From equations (i) and (ii),

55x –275 = 50x–150

55x –50x = 275 - 150

5x = 125 ⇒ x = $125/5$ = 25

Speed of the train = 25 kmph

Here, $S_1 = 3, S_2 = 5, t_1 = 10/3600 , t_2 = 11/3600$

Speed of train = ${t_1S_1 - t_2S_2}/{t_1 - t_2}$

= ${{3 × 10}/3600 - {5 × 11}/3600}/{10/3600 - 11/3600}$

= ${-25}/3600 × 3600/{- 1}$ = 25 m/sec

Answer: (c)

Speed of train = 36 kmph

= $({36 × 5}/18)$ m./sec. = 10 m./sec.

Required time = $\text"Length of train"/ \text"Speed of train"$

= $60/10$ = 6 seconds