JEE MAIN - Physics (2019 - 12th January Morning Slot - No. 26)
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 :
$${{25} \over {11}}$$
$${3 \over 2}$$
$${{11} \over 5}$$
$${5 \over 2}$$
Explanation
The total distance to be travelled by the train is
60 + 120 = 180 m.
When the trains are moving in the same direction, relative velocity is
v1 – v2 = 80 – 30 = 50 km hr–1
So time taken to cross each other,
t1 = $${{180} \over {50 \times {{{{10}^3}} \over {3600}}}}$$
When the trains are moving in opposite direction, relative velocity is
|v1 – (–v2 )| = 80 + 30 = 110 km hr–1
$$ \therefore $$ Time taken to cross each other
t2 = $${{180} \over {110 \times {{{{10}^3}} \over {3600}}}}$$
$$ \therefore $$ $${{{t_1}} \over {{t_2}}} = {{{{180} \over {50 \times {{{{10}^3}} \over {3600}}}}} \over {{{180} \over {110 \times {{{{10}^3}} \over {3600}}}}}}$$ = $${{11} \over 5}$$
When the trains are moving in the same direction, relative velocity is
v1 – v2 = 80 – 30 = 50 km hr–1
So time taken to cross each other,
t1 = $${{180} \over {50 \times {{{{10}^3}} \over {3600}}}}$$
When the trains are moving in opposite direction, relative velocity is
|v1 – (–v2 )| = 80 + 30 = 110 km hr–1
$$ \therefore $$ Time taken to cross each other
t2 = $${{180} \over {110 \times {{{{10}^3}} \over {3600}}}}$$
$$ \therefore $$ $${{{t_1}} \over {{t_2}}} = {{{{180} \over {50 \times {{{{10}^3}} \over {3600}}}}} \over {{{180} \over {110 \times {{{{10}^3}} \over {3600}}}}}}$$ = $${{11} \over 5}$$
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