Question Video: Finding the Relative Velocity between Two Bodies Moving in Opposite Directions in Vector Form Mathematics

Video Transcript

Two cars A and B are moving in opposite directions on the same road at 62 kilometers per hour and 31 kilometers per hour, respectively. Given that 𝐞 is a unit vector in the direction of movement of car A, determine the velocity of car A relative to car B.

We’re asked to determine the relative velocity of car A with respect to car B and given that 𝐞 is a unit vector in the direction of car A. We’re told the car A is moving at 62 kilometers per hour and car B is moving at 31 kilometers per hour in the opposite direction. The velocity of car A is then 62𝐞. And since car B is moving in the opposite direction, its velocity 𝐕 B is negative 31𝐞.

Now recalling that for two bodies A and B moving with velocities 𝐕 A and 𝐕 B, respectively, the relative velocity of A with respect to B is 𝐕 AB and that’s 𝐕 A minus 𝐕 B. In our case, that’s 62𝐞, which is 𝐕 A, minus negative 31𝐞, which is 𝐕 B. 62 minus negative 31 is 62 plus 31. And so we have 93𝐞. The velocity of car A relative to car B is 93𝐞 kilometers per hour.