## Akoranga 10 Mahi Tuatahi

- Yssy travels 30km south and then 20km west. Draw a vector diagram to show her total
**displacement (resultant)**. - Max and Lena are pushing a box. Max is pushing it with force 500N to the right, and Lena is pushing it with force 400N up. Draw a vector diagram to show the
**net (resultant) force**. - Phoebe is flying at $7ms^{-1}$ east. Phoebe changes direction so she flying at $7ms^{-1}$ south. Draw a vector diagram to show the
**change in velocity**of Phoebe.

## Te Whāinga Ako

- Be able to describe the motion of an object undergoing projectile motion.

Write the date and te whāinga ako in your book

### Whakamātau/Experiment

- First, watch this clip and count how many seconds the student was in the air for
- Second, open Google Classroom and find the Projectile Motion whakamātau/experiment.

## Projectile Motion

Motion under gravity.

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### Pātai: Describing Velocity

To get into projectile motion we first need to correctly describe the *velocity* and *acceleration* of an object in motion.

A ball is thrown vertically upwards. **In pairs on a whiteboard, draw a diagram and describe the direction of the ball’s velocity and acceleration when:**

- It is going up,
- it is going down,
- it is at the highest point.

#### Whakatika

### Forces on The Ball

- We assume that friction force is negligible (we ignore it).
- Therefore,
*the only force*acting upon the ball while in the air is the**weight force**.

\begin{aligned} F_{net} = F_{weight} \end{aligned}

The ball experiences a constant downwards acceleration ($-9.8ms^{-2}$) at all times, and **no** acceleration in the horizontal direction.

### Acceleration Due to Gravity

\begin{aligned} g = 9.8ms^{-2} \end{aligned}

The acceleration of any object in the air without its own power source.

## Mahi Tuatahi

Calculate the height that your ball reached yesterday in your experiment

### So, Projectile Motion

- An object that moves through the air
**without its own power source**, - only force acting upon it is the
**weight force**, - always experiencing
**downward acceleration of $9.8ms^{-2}$**, - motion up/down is symmetrical.

### Pātai Tahi

A ball is thrown upwards with an initial speed of $161.3km/hr$ ($44.8ms^{-1}$).

- How long does it take for the ball to reach its highest point?
- How high does the ball rise?

**Remember:** Knowns, Unknowns, Formula, Substitute, Solve

### Pātai Rua

Lachie kicks a rugby ball straight upwards. It is in the air for $10.6s$ before it hits the ground.

- What is the initial velocity of the ball?
- How high does the ball rise?

**Remember:** Knowns, Unknowns, Formula, Substitute, Solve

### Pātai Toru

Angus is going cliff diving. He jumps and falls for $3.4s$ before hitting the water below.

- What is his
**initial velocity**? - What is his
**acceleration**? - What is his
**final velocity**(as he hits the water)? - How
**high**is the cliff?

**Remember:** Knowns, Unknowns, Formula, Substitute, Solve

### Whakawai/Practise

- Complete Worksheet 5
- Textbook Activity 8C Q1-6
**Manatu/Remember**: Homework Kinematics Q1 due Tuesday!

## 2-D Kinematics: The Cannon Ball Question

A cannon ball is fired horizontally from the top of a hill. The velocity of the cannon ball is split into $x$ and $y$ components, which are independent of each other.

### Vertical Motion

**Recall:**once in motion, the only force acting upon the cannon ball is the**weight force**. We are assuming friction is negligible.- Therefore: the cannon ball is experiencing a constant downward acceleration of $g=-9.8ms^{-2}$.

### Horizontal Motion

**Recall:**once in motion, the only force acting upon the cannon ball is the**weight force**. We are assuming friction is negligible.- Therefore, the cannon ball does not experience any forces in the horizontal direction. Therefore it does not accelerate in the horizontal direction.

### Summary

\begin{aligned} Projectile Motion = Vertial Motion + Horizontal Motion \end{aligned}

## Vertical Motion

Constant downwards acceleration of $-9.8ms^{-2}$.

## Horizontal Motion

No acceleration, therefore constant speed. $v_{i} = v_{f}$

# Thought Whakamātau/Experiment

If the cannon ball is fired with a **greater horizontal velocity** will it take longer to hit the ground?

# Pātai

A marble rolls of a desk of height 1.25m and with $v_{x} = 1.6ms^{-1}$.

- Calculate the
**duration of the fall**. - During the fall, how far does the marble travel
**horizontally**? - How far does the marble travel if $v_{x} = 3ms^{-1}$?