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  • A passenger train of length 60 m travels at a speed of 80 km/hr. Another 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 t

A passenger train of length 60 m travels at a speed of 80 km/hr. Another 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 second train when : (i) they are moving in the same direction and (ii) when they are moving in the opposite direction is

Option: 1

\frac{25}{11}


Option: 2

\frac{3}{2}


Option: 3

\frac{5}{2}


Option: 4

\frac{11}{5}


Answers (1)

best_answer

The total distance to be traveled by the train is \mathrm{60+120=180m}

When the trains are moving in the same direction, relative velocity is

v_1-v_2=80-30=50 \mathrm{kmh}^{-1}

So, time taken to cross each other, 

t_1=\frac{180}{50 \times \frac{10^3}{3600}}=\frac{18 \times 18}{25} \mathrm{~s}

When the trains are moving in the opposite direction, relative velocity is

\left|v_1-\left(-v_2\right)\right|=80+30=110 k m h^{-1}

So, the time taken to cross each other

t_2=\frac{180}{110 \times \frac{1000}{3600}}=\frac{18 \times 36}{110} \mathrm{~s}

Ratio, \frac{t_1}{t_2}=\frac{\frac{18 \times 18}{25}}{\frac{18 \times 36}{110}}=\frac{11}{5}

Posted by

HARSH KANKARIA

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