Question

Two trains are travelling away from a common station at speeds of u and 2u, in directions that are at an angle 60° to each other. What is the velocity of the train with speed 2u relative to an observer in the other train?

Answer 1

using concept of relative velocity we can solve this question...

see attachment....

_____________________________

hope it will help u

Answer 2

Let the Two trains X and Y are travelling away from a common station at speeds of u and 2u at an angle of 60° respectively.

Now according to question 
let an observer in the other train i.e train Y

By the diagram the components of velocity w.r.t x and y- axis is given as :-

$V_{A}$ = 2ucos60°(i^) + 2usin60°(j^)
                           = 2u* 1/2(i^) + 2u* √3/2(j^)
                           =u(i^) + √3u(j^)
                           
$V_{B}$ = u(i^)

For  velocity of the train with speed 2u relative to an observer in the other train -
$V_{AB}$ = $V_{A}$ - $V_{B}$
                             = u(i^) + √3u(j^) - u(i^)
                             = √3u(j^)

In magnitude √3u m/s it is the velocity of the train with speed 2u relative to an observer in the other train.

----------------------------------------------------------------------------------------------------------------
Best of luck ;)
ROYALJATT