Kinematics 3 Question 4
4. A passenger train of length $60 m$ travels at a speed of $80 km / hr$. Another freight train of length $120 m$ travels at a speed of $30 km / hr$. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is
(2019 Main, 12 Jan I)
(a) $\frac{3}{2}$
(b) $\frac{25}{11}$
(c) $\frac{11}{5}$
(d) $\frac{5}{2}$
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Answer:
Correct Answer: 4. (c)
Solution:
- When trains are moving in same direction relative speed $=\left|v _1-v _2\right|$ and in opposite direction relative speed
$$ =\left|v _1+v _2\right| $$
Hence, ratio of time when trains move in same direction with time when trains move in opposite direction is
$$ \frac{t _1}{t _2}=\frac{\frac{l _1+l _2}{\left|v _1-v _2\right|}}{\frac{l _1+l _2}{\left|v _1+v _2\right|}}=\frac{\left|v _1+v _2\right|}{\left|v _1-v _2\right|} $$
where, $l _1+l _2=$ sum of lengths of trains which is same as distance covered by trains to cross each other
So, $\quad \frac{t _1}{t _2}=\frac{80+30}{80-30}=\frac{110}{50}=\frac{11}{5}$
