QUESTION THREE a. Define Impulse and Momentum b. Name the three (3) types of collisions c. Calculate the height to which the ball will bounce to in the: i. First bounce ii. Second bounce

Here are the solutions to Question Three.

Question 3a) Define the following terms:

i. Impulse
Impulse is the change in momentum of an object. It is also defined as the product of the net force acting on an object and the time interval over which the force acts.

$$\text{Impulse} = \Delta p = F \Delta t$$

ii. Momentum
Momentum is a measure of the mass and velocity of an object. It is a vector quantity defined as the product of an object's mass and its velocity.

$$p = mv$$

Question 3b) Name the three (3) types of collisions.

The three types of collisions are:

1. Elastic collision: A collision in which both momentum and kinetic energy are conserved.
2. Inelastic collision: A collision in which momentum is conserved, but kinetic energy is not conserved (some kinetic energy is lost, usually as heat or sound).
3. Perfectly inelastic collision: A type of inelastic collision where the colliding objects stick together after impact, moving as a single combined mass.

Question 3c) A rubber ball is allowed to fall freely in the earth's gravitational field from a height of 4.0 m above a flat horizontal surface. The coefficient of restitution between the ball and the surface is 0.60. Calculate the height to which the ball will bounce to in the:

Given:
Initial height, $h_0 = 4.0 \text{ m}$
Coefficient of restitution, $e = 0.60$

The relationship between the height of a bounce ($h_n$) and the height of the previous bounce ($h_{n-1}$) is given by the formula:

$$e = \sqrt{\frac{h_n}{h_{n-1}}}$$

Squaring both sides, we get:

$$e^2 = \frac{h_n}{h_{n-1}}$$

Therefore, the height of the current bounce is:

$$h_n = e^2 h_{n-1}$$

i. First bounce