Question

A girl is running toward the front of a train at 10 m/s. If the train is going 75 m/s on the Southbound tracks, what is the speed of the train relative to the girl?

Answer 1

Answer:

velocity of the train with respect to girl is 85 m/s

Explanation:

As we know that girl is moving towards the train in front of it with speed

$v_1 = 10 m/s$

also we know that the speed of the train towards the girl is

$v_2 = 75 m/s$

Now we know that relative velocity of the train with respect to girl is given as

$\vec v_{tg} = \vec v_t - \vec v_g$

here let say the velocity of train is positive while girl is running opposite to train so its velocity is negative

$\vec v_{tg} = 75 m/s - (-10 m/s)$

$\vec v_{tg} = 85 m/s$

Answer 2

We can take as positive direction the direction of the train, and as negative direction the direction of the girl. The speed of the train relative to the girl will be given by the difference between the two velocities:
$v' = v_t - v_g$
which means
$v'=75 m/s - (-10 m/s)=85 m/s$