Question

A railroad flatcar is travelling to the right at speed of 13 m/s relative to an observer on the ground. Someone is riding a motor scooter on the flatcar. What is the velocity of motor scooter relative to the flatcar if its relative velocity to the observer on the ground is (a) 18 m/s to the right? (b) 3 m/s to the left? (c) zero?

Answer 1

The velocity of the scooter relative to the flatcar is given as follows (see https://en.wikipedia.org/wiki/Velocity-addition_formula#Galilean_relativity):

$$u' = u-v$$

where $u$ is the velocity of the scooter relative to the observer, and $v = 13m/s$ is the velocity of the flatcar relative to the observer.

Let's choose the direction to the right as a positive direction. Then:

a) $u = 18m/s$.

$$u' = 18m/s-13m/s = 5m/s$$

b) $u = -3m/s$ (minus because it is directed to the left).

$$u' = -3m/s - 13m/s = -16m/s$$

c) $u = 0m/s$.

$$u' = 0 - 13m/s = -13m/s$$

Answer. a) 5m/s to the right, b) 16m/s to the left, c) 13m/s to the left.