A train is moving with a velocity of \( 100 km h ^{-1} \) in the North-East direction. If another train is moving with a velocity of \( 50 km h ^{-1} \) in the North-West direction, then what is the relative velocity of the second train w.r.t. the first train? (1) \( 150 km / hr \) (2) \( 50 km / hr \) (3) \( 112 km / hr \) (4) \( 84 km / hr \)

Question

A train is moving with a velocity of 100 kmph in the North-East direction. If another train is moving with a velocity of 50 kmph in the North-West direction, then what is the relative velocity of the second train w.r.t. the first train? 

(1) 150 km / hr  (2) 50 km / hr (3)  112 km / hr \) (4)  84 km / hr \)

Answer 1

Given that,

Velocity of train = 100 km/hr

Velocity of another train = 50 Km/hr

We need to calculate the relative velocity of second train with respect to the first train

Using formula of relative velocity

\(V_{AB} = \sqrt {(OA)^2 + (OB)^2}\)

Put the value into the formula

\(V_{AB} = \sqrt {100^2 + 50 ^2}\)

\(V_{AB} =111.80\,km/h\)

Hence, The relative velocity of second train with respect to the first train is 111.80 km/hr.