Vectors

Dear Samarth,
Do you remember the picture I showed about an air-plane which was flying at an angle although it wanted to go straight because there was a wind pushing it?

What about the life saver that was dropped from the air-plane, how it was moving both forward at the same time it was going down?

Vectors helps up with breaking such problems into easy pieces. So for example, we break speed into vertical speed and horizontal speed and then it becomes easy for us to find things like how much distance the air-plane covered in 10 seconds and how far the life saver dropped in 10 seconds. For horizontal distance if we know that air-plane travels 100 meters in 1 second then it will travel 1000 meters in 10 seconds. Right?

We do the same for vertical and say in 10 seconds it drops 500 meters. Then we know where the life saver will drop in 10 seconds.

See the picture below:

Let's say a car is moving in the direction of the line marked with SPEED. We break the vertical speed as VSPEED and horizontal speed as HSPEED. So we can say the speed of the car is

HSPEED*x + VSPEED*y

It is the sum of vertical and horizontal speed. The car is actually moving along SPEED, which is sum of speed in x-direction and speed in y-direction. Does that make sense?

A vector in essence has both speed and direction. When you add two vectors, you add the individual direction together, but you can't add the x-direction variable with y-direction variable.

Here's a small problem. Can you tell which boat will reach the other shore first?

Love
Papa