During a race, two cars 𝐴 and 𝐵 are moving in a straight line in the same direction. Car 𝐴 is chasing car 𝐵. Car 𝐴 moves with a uniform velocity of 250 kilometers per hour, and the driver of car 𝐵 sees that car 𝐴 seems to be moving towards him with velocity 180 kilometers per hour. What is the actual velocity of car 𝐵?
We will begin by sketching a diagram of the race.
We are told that the two cars are moving in a straight line in the same direction and that car 𝐴 is chasing car 𝐵. We know that the velocity of car 𝐴 is 250 kilometers per hour. And we are trying to calculate the velocity of car 𝐵. We are also told in the question that the driver of car 𝐵 sees that car 𝐴 seems to be moving toward him with velocity 180 kilometers per hour. This is the relative velocity.
We know that this relative velocity, written 𝑉 sub 𝐴𝐵, is equal to the velocity of 𝐴 minus the velocity of 𝐵 for any two bodies 𝐴 and 𝐵 moving along the same one-dimensional axis. Substituting in our values from the question, we have 180 is equal to 250 minus 𝑉 sub 𝐵. We can then add 𝑉 sub 𝐵 to both sides of our equation and subtract 180 from both sides. 𝑉 sub 𝐵 is equal to 250 minus 180. This is equal to 70 kilometers per hour.
The actual velocity of car 𝐵 is 70 kilometers per hour.