By Keiji Oenoki [physics@amersol.edu.pe]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.

### Section 1. Dropping a Ball

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/s2. 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.

 Displacement Velocity Acceleration x-direction d = 0 v = 0 a = 0 y-direction v = at a = -9.8

### Section 2. Throwing a Ball Horizontally

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.

 Displacement Velocity Acceleration x-direction d = At v = A a = 0 y-direction v = at a = -9.8

### Section 3. Throwing a 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.

 Displacement Velocity Acceleration x-direction d = Vx * t v = Vx a = 0 y-direction v = Vy + at a = -9.8

### Section 4. Bouncing a Ball

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:

V2 = e * V1

where V1 is the velocity before collision, V2 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:

### Section 5. Chapter 7 Quiz

This is the last quiz of Lesson 1. Good luck!

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Colegio Franklin Delano Roosevelt
July, 1997