Video Transcript
If 𝐯 sub A is equal to 60𝐞 and 𝐯 sub B is equal to negative 40𝐞, then 𝐯 sub AB is equal to what 𝐞.
In this question, we are given the velocity vectors of A and B in terms of the unit vector 𝐞. And we’ve been asked to find the relative velocity of A with respect to B. We know that this is equal to the velocity of A minus the velocity of B for two bodies A and B moving along the same one-dimensional axis. In this question, this is equal to 60𝐞 minus negative 40𝐞, which is the same as adding 40𝐞 to 60𝐞. The velocity of A relative to B is therefore equal to 100𝐞. And the missing number from our question is 100.
This situation can be represented on a diagram as shown. As the two bodies are traveling in the opposite direction, the magnitude of their relative velocity will be greater than the magnitude of their individual velocities. This suggests that the relative velocity of A with respect to B of 100𝐞 is correct.
