First slide

Relative velocity in 1-d

Question

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36km/hour and 72km/hour respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8km/hour. Speed (in $m s^{- 1}$ ) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

Easy

A

$29.5 m s^{- 1}$
B

$28.5 m s^{- 1}$
C

$31.5 m s^{- 1}$
D

$30.5 m s^{- 1}$

Solution

$V_{A} = 10 m / s V_{B} = - 20 m / s$
Velocity of person w.r.t train A, $V_{P A} = - 0.5 m / s$
$∴$ Velocity of person
$\Rightarrow V_{P} = V_{P A} + V_{A} = - 0.5 + 10 = 9.5 m / s$
And $V_{P B} = V_{P} - V_{B} = 9.5 - (- 20) = 29.5 m / s$

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