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2 identical trains take 3 sec to pass 1 another when going in the opposite direction but only 2.5 sec if speed of 1 is increased by 50%.The time one would take to pass the other when going in the same direction at their original speed is? 2 identical trains take 3 sec to pass 1 another when going in the opposite direction but only 2.5 sec if speed of 1 is increased by 50%.The time one would take to pass the other when going in the same direction at their original speed is?
let train A is moving along positie x axis with vel = +V train B along negative x axis = -U vel of train A with respect B is = V-(-U) = V+U let S be distance S=(V+U)3 S=(V + U + U/2)2.5 => S= (V+3/2U)2.5 get v and u in terms of S then apply S=(V-U)t (now V along and u in same direction v=V-U) and find t may be answer 30/4 secs
let train A is moving along positie x axis with vel = +V
train B along negative x axis = -U
vel of train A with respect B is = V-(-U) = V+U
let S be distance
S=(V+U)3
S=(V + U + U/2)2.5
=> S= (V+3/2U)2.5
get v and u in terms of S
then apply S=(V-U)t (now V along and u in same direction v=V-U)
and find t
may be answer 30/4 secs
working in ref frame attached to 2, velocity of 1 wrt 2= v1+v2 let length of train be x metres each. therefore time taken to cross each other= 2x/v1+v2=3 => 2x= 3v1+3v2----------------------------------------------(1) Case 2: velocity of 1= v1+50v1/100=3v1/2 now, time taken to cross each other= 2x -------------- = 2.5 3v1/2- v2 => 2x= 2.5v2+ 7.5v1/2---------------(2) equating (1) and (2) 3v1+3v2= 2.5v2+7.5v1/2 => 1.5v1/2= v2--------------------------------(3) now if they move in same direction: velocity of 1 wrt 2= v1-v2 time taken to cross each other= 2x/v1-v2 = 2x/v1-0.75v1 (from 3) = 2x/0.25v1 = 3v1+3 v2/ 0.25v1 (from 1) = 3v1+ 0.75v1/0.25v1 (from 3) = 3.75v1/0.25v1 = 15 sec all the best!
working in ref frame attached to 2,
velocity of 1 wrt 2= v1+v2
let length of train be x metres each.
therefore time taken to cross each other= 2x/v1+v2=3
=> 2x= 3v1+3v2----------------------------------------------(1)
Case 2:
velocity of 1= v1+50v1/100=3v1/2
now, time taken to cross each other= 2x -------------- = 2.5
3v1/2- v2
=> 2x= 2.5v2+ 7.5v1/2---------------(2)
equating (1) and (2)
3v1+3v2= 2.5v2+7.5v1/2
=> 1.5v1/2= v2--------------------------------(3)
now if they move in same direction:
velocity of 1 wrt 2= v1-v2
time taken to cross each other= 2x/v1-v2
= 2x/v1-0.75v1 (from 3)
= 2x/0.25v1
= 3v1+3 v2/ 0.25v1 (from 1)
= 3v1+ 0.75v1/0.25v1 (from 3)
= 3.75v1/0.25v1
= 15 sec
all the best!
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