When in going east at 10 kmph, a train moving with constant velocity appears to be moving exactly ‘north-east’. When my velocity is increased to 30 kmph east it appears to be moving north. What spped should i move north so that train appears to be moving exactly south-east ?

Dear student,

Since while moving east with, the train seems to move in NE, the north and East componets of train are such that


When moving East with velocity, the train seems to move northwards.

Hence the east component of train must be

Hence

Now after moving nortward with speed, the train seems to move in South-East.
Hence