Two bodies are moving on the same line. When they move away from each other the distance between them changes for 16m in a time interval of 3 s (Δd1 = 16 m ; Δt1 = 3 s). When they move towards each other the distance between them changes for 3 m in a time interval of 3 s (Δd2 = 3 m ; Δt2 = 3 s). What are the respective speeds of the two bodies?
Basic kinematic and Galilean relativity equations.
The Attempt at a Solution
So, I've reasoned that if the speeds of the bodies are constant, then in both cases, whether they are moving towards or away each other, the relative speed should be the same, because in both cases it is given by Vrelative=V1+V2, since their respective velocity vectors point in different directions in both cases. From that it follows that if the relative speeds are the same in both cases, then this equality holds Δd1/ Δt1 = Δd2/Δt2 , but it obviously does not when the numbers given in the problem are plugged in.
The solution in the book assumes that the relative speeds are not the same in the two cases, saying that in the case when they move away from each other the relative speed is given by Vrelative=V1+V2 but however in the case when they move towards each other the relative speed is given by Vrelative=V1-V2 which I don't understand why.