Question

A train is moving with uniform velocity on a straight track. A boy moving at 4 km/h due east observes that the train is moving due north. Another boy moving at 1 km/h due south claims that the train is moving towards north-east. What is the speed of the train in ground frame ?

Answer 1

Answer:

5km/h

Explanation:

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Answer 2

Answer: Speed of train in ground frame is 5 km/h.

Explanation:

i and j are unit vectors in X and Y direction

Velocity of train in ground frame = Veocity of boy1 + Relative velocity of train with respect to boy1

Velocity of train in ground frame =  4 i + u j

Velocity of train in ground frame = Veocity of boy2 + Relative velocity of train with respect to boy2

Velocity of train in ground frame =  -1 j + ( v/√2 i + v/√2 j )

                                                      =  v/√2  i  + ( v/√2 - 1) j

The train will have a single velocity at a given time, therefore,

⇒ v/√2  i  + ( v/√2 - 1) j  = 4 i + u j

⇒ v/√2 =  4

⇒ v = $4\sqrt{2}$

Velocity of train in ground frame = v/√2  i  + ( v/√2 - 1) j =   4 i + 3 j

Speed of train = $\sqrt{4^{2} +3^{2} }$ km/h

Speed of train in ground frame = 5 km/h

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