Question Video: Calculating the Relative Velocity of a Particle with Respect to Another Particle Mathematics

Video Transcript

If 𝐕 sub 𝐴 is equal to 50𝐞 and 𝐕 sub 𝐵 is equal to negative 15𝐞, then the relative velocity 𝐕 sub 𝐴𝐵 is equal to what 𝐞.

In this question, we’re given the velocity vectors of 𝐴 and 𝐵. And we are asked to find the coefficient of 𝐞 and the velocity of 𝐴 relative to 𝐵. Since both velocity vectors are given in terms of vector 𝐞, we know that both bodies are moving along the same one-dimensional axis. However, they are moving in opposite directions. Body 𝐴 is moving in the positive direction and body 𝐵 in the negative direction. We recall that the relative velocity of 𝐴 with respect to 𝐵 is equal to the velocity of 𝐴 minus the velocity of 𝐵. Substituting the values we’re given, this is equal to 50𝐞 minus negative 15𝐞, which is the same as adding 15𝐞 to 50𝐞.

The relative velocity of body 𝐴 with respect to 𝐵 is therefore equal to 65𝐞. And we can therefore conclude that the missing number is 65. It is worth noting that if two bodies are traveling in the opposite direction, the magnitude of their relative velocity will be greater than the individual magnitudes of the velocities. In this case, 65 is greater than both 50 and 15 and is equal to the sum of these values.