This
is the last chapter of Lesson 1. In this Lesson, you
have learned how objects move and why. This chapter
will summarize everything you learned. In this
chapter, we will observe how a ball behaves under
different conditions, and review what we have studied
so far.

Let's start with the simplest thing: dropping a
ball. We know that the ball will fall straight down
when you drop it, since we applied no force on
x-direction. The velocity on x-direction is zero and
the acceleration is also zero.

The ball will fall because of gravity. We know
that the force of gravity applies to any object. The
ball's acceleration on y direction is -9.8 m/s^{2}.
Its initial velocity is zero.

The velocity of the ball is not dependent on its
mass. The velocity is, however, dependent on its
surface area and air resistance. We ignore the air
resistance since it can make things complicated.

The following illustrates how the ball will fall:

The following table shows how to calculate
position, velocity, and acceleration of the ball at a
given time t.

Next, think about throwing a ball in horizontal
direction with an initial velocity of A. Then, the
velocity of the ball on x direction is A, and it will
stay unchanged since there is no force that will
influence its movement in horizontal direction. The
acceleration on x direction is zero, because the net
force on the ball is zero.

The acceleration of the ball on y direction is
-9.8 m/s2, and its initial velocity is zero. The ball
will behave like this:

You can change the initial velocity on x direction
and see how it behaves.

The following table shows how to calculate
displacement, velocity, and acceleration of the ball.

Next, think about how a cannon ball flying through
the air. Let's say the ball was thrown with an
initial velocity of V with an angle of a.

You can break down V into Vx and Vy. Vx = cos a *
V and Vy = sin a * V.

The velocity on x direction is Vx. The
acceleration on x is zero.

The velocity on y direction is Vy. The
acceleration on y is -9.8 m/s2.

The following will simulate the movement of the
ball:

You can change the initial velocity and angle, and
see how far the ball travels. Note that the ball will
travel the farthest when the angle is 45 degrees.

When you throw a ball on a rug, it doesn't bounce
much. When you throw the ball to floor, it bounces
higher. The reason is in the coefficient of bounce.

Whenever two objects collide, the following
equation is true:

V_{2} = e * V_{1}

where V_{1} is the velocity before
collision, V_{2} is the velocity after
collision, and e is a constant. This constant e is
called the coefficient of bounce, which ranges from 0
to 1. When there is no friction between the two
objects, e = 1. As the friction increases, the value
of e approaches to 0.

We can say that a rug has a lower coefficient of
bounce than floor. Probably e = 0.2 in a rug, and e =
0.8 on floor.

You can experiment with the coefficient of bounce
below: