Velocity-addition formula

So, imagine you are playing catch with a friend. You throw a ball to them and they throw it back to you. When you throw the ball, it has a certain speed, let's call it "velocity".

Now, imagine that you are both standing on a train that is also moving. You throw the ball again, but this time, both you and the ball are moving because of the train.

The question is, how fast is the ball moving now? Is it just the speed you threw it at, or is it faster because of the train?

To figure this out, we need to use something called the "velocity-addition formula". This formula helps us calculate how fast something is moving when we add two velocities together.

Here's how it works:

Let's say the train is moving at 10 kilometers per hour (kph) and you throw the ball at 5 kph. We need to find out how fast the ball is moving now that it's on the train.

You start by adding the two velocities together:

10 kph (train) + 5 kph (ball) = 15 kph

So, the ball is now traveling at 15 kph because we added its original velocity to the velocity of the moving train.

This is helpful when we are trying to figure out how fast objects are moving in different situations, like when we are in a car, on a plane, or even in space.

In summary, the velocity-addition formula helps us calculate how fast something is moving when we add two velocities together, and it's like playing catch on a moving train - the ball is moving faster because of the velocity of the train we added to its original velocity.