Question

Two trains A and B, 100m and 60m long, are moving in opposite directions on parallel tracks. the velocity of the shorter train is 3 times that of longer one. if the train takes 4s to cross each other, the velocities of the trains are

Answer 1

Length of the First train (A) = 100 m.

Length of the second train (B) = 60 m.

∵ $V_B = 3 V_A$

Since, the train are crossing each other in opposite direction,

∴ Relative Distance = 100 + 60

= 160 m.

Now, Relative Velocity $V_{AB}$ = 160/4

= 40 m/s.

Now, Using the Formula,

$V_{AB} = V_A + V_B$ [Since, trains are moving in opposite direction].

40 = $V_A + 3V_A$

⇒ $4V_A = 40$

∴ $V_A = 10$

∴ $V_B = 30$

Hence, the Velocity of the train A is 10 m/s. and that of second train is 30 m/s.

Hope it helps.

Answer 2

Explanation:

Length of the First train (A) = 100 m.

Length of the second train (B) = 60 m.

∵ V_B = 3 V_AV

B

=3V

A

Since, the train are crossing each other in opposite direction,

∴ Relative Distance = 100 + 60

= 160 m.

Now, Relative Velocity V_{AB}V

AB

= 160/4

= 40 m/s.

Now, Using the Formula,

V_{AB} = V_A + V_BV

AB

=V

A

+V

B

[Since, trains are moving in opposite direction].

40 = V_A + 3V_AV

A

+3V

A

⇒ 4V_A = 404V

A

=40

∴ V_A = 10V

A

=10

∴ V_B = 30V

B

=30

Hence, the Velocity of the train A is 10 m/s. and that of second train is 30 m/s.

Hope it helps.