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Projectile Motion

Akoranga 10 Mahi Tuatahi

  1. Yssy travels 30km south and then 20km west. Draw a vector diagram to show her total displacement (resultant).
  2. 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.
  3. 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

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

Write the date and te whāinga ako in your book


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:

  1. It is going up,
  2. it is going down,
  3. it is at the highest point.

Whakatika

Velocity

Acceleration


Forces on The Ball

\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


Pātai Tahi

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

  1. How long does it take for the ball to reach its highest point?
  2. 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.

  1. What is the initial velocity of the ball?
  2. 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.

  1. What is his initial velocity?
  2. What is his acceleration?
  3. What is his final velocity (as he hits the water)?
  4. How high is the cliff?

Remember: Knowns, Unknowns, Formula, Substitute, Solve


Whakawai/Practise


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.

Source


Vertical Motion


Horizontal Motion


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 $v_{x} = 1.6ms^{-1}$.

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