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What is the connection?

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Projectile motion

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Which equations can be used to describe the motion of projectiles?

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What force acts on an upward moving projectile? First, think about…

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When the ball is stationary, what forces are acting on it?

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Remove the hands and…? What happens to the ball? What forces are acting on the ball? Air resistance is negligible

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Describe the motion using the words velocity, acceleration and displacement. Explain in terms of forces.

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Sketch the velocity–time and acceleration–time graphs of the motion. Include values on the axes.

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What force acts on an upward moving projectile?

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Initial vertical velocity of a ball dropped from a height?

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A ball thrown up in the air. Vertical velocity at maximum height?

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A ball thrown up in the air. Is it on its way up or down?

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For a ball which is thrown up and allowed to fall back to exactly the same point… …the downward motion will mirror the upward motion.

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How will initial vertical velocity and final vertical velocity compare in magnitude? In direction?

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Up or down, what is the acceleration of the ball?

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–9.8 m s –2

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Remember: air resistance is negligible

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Describe the horizontal motion of this tennis ball. Are there horizontal forces acting on the ball? Does the horizontal velocity change?

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Summarise your learning for a vertical projectile Direction of motion ForcesVelocityAcceleration Horizontal Vertical

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Summarise your learning for a vertical projectile Direction of motion ForcesVelocityAcceleration Horizontal Air resistance negligible so no forces in the horizontal Constant (in this case 0 m s –1 ) None Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s –2

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Another projectile situation…

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Picture a motorcyclist…

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…on the top of a tall building about to perform a death- defying stunt of incredible skill. DONT TRY THIS AT HOME

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Predict her path once she launches off the building.

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Predictions for a horizontal projectile Direction of motion ForcesVelocityAcceleration Horizontal Vertical

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Just as she launches…someone switches off gravity! Predict her path with no gravity. Remember: air resistance is negligible.

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Switching gravity back on…

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Virtual Higher Physics Mechanics and Properties of Matter Projectile Motion Video of projectile motion (Motion Grapher Simulations: ball projected horizontally (horizontal component) ball projected horizontally (vertical component))

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Summarise your learning for a horizontal projectile Direction of motion ForcesVelocityAcceleration Horizontal Vertical

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Summarise your learning for a horizontal projectile Direction of motion ForcesVelocityAcceleration Horizontal Air resistance negligible so no forces in the horizontal ConstantNone Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s –2

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Class challenge! Can you save the motorcyclist from being eaten?

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Do you believe in physics? Do you trust the equations of motion? Would you jump over the crocodiles based on the equations?

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Verifying the equations of motion How could you use the equipment to verify the equations of motion?

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Okay then…some hints What determines the horizontal displacement? What determines the time spent in the air? What is the initial vertical velocity of a horizontal projectile?

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Class challenge Use the equipment to determine the horizontal velocity with which the ball leaves the launcher. Safety warnings (c) Pasco Feedback

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Class challenge How well have you understood? Calculate the horizontal velocity required to save the motorcyclist from being eaten.

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What formula can be used to calculate the horizontal displacement of an object fired horizontally if horizontal velocity and time of flight are known? s h = u h t + ½at 2 horizontal displacement (m) horizontal velocity (m s –1 ) time of flight (s)

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What formula can be used to calculate the vertical displacement of an object fired horizontally? s v = u v t + ½at 2 vertical displacement (m) initial vertical velocity (m s –1 ) time of flight (s)

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Which will hit the ground first? Predict, observe, explain Are the two balls identical? Does it matter?

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A thought experiment: the frictionless marble on the frictionless surface The marble is travelling horizontally at 5 m s –1. Describe its motion at: 0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s

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A thought experiment: the frictionless marble on the frictionless surface How can we calculate the horizontal displacement at: 0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s

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The frictionless marble dropped off the Eiffel Tour (into the air- resistance-free Paris sky) How can we calculate the vertical displacement at: 0.1 s, 0.2 s, 0.3 s, 0.4 s, 0.5 s, 0.6 s, 0.7 s, 0.8 s, 0.9 s, 1.0s

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The frictionless marble: the complete picture Using Excel, we can plot a graph of horizontal displacement against vertical displacement.

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Observe and explain

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Still dont believe the independence of horizontal and vertical components? Two more possibilities…

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A traditional method involving: five small cans, open at each end (take care of sharp edges) a white board with graph paper (traditional not interactive) a method of fixing cans to the board. a ball a good aim.

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Position the cans so the ball, when projected horizontally, will fall through each can.

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A higher technology method involving: The photo shown above must have been faked. Explain! © Pasco Feedback

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Group thinking What do you already know that you can apply to projectiles fired at an angle? Think forces, vectors, equations…

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© PASCO Feedback

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Hints! Any vector can be resolved into its horizontal and vertical components.

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The horizontal component launch velocity (m s –1 ) θ

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The vertical component launch velocity (m s –1 ) θ

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Calculate the launch velocity. Using this, resolve the vectors and calculate the range of the projectile. The range is how far the projectile travels horizontally. © PASCO Feedback

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From the measured range, calculated what the launch velocity should be. Are the values the same? Explain! © PASCO Feedback

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Predict, then determine experimentally and by calculation which angle will give the greatest range for a fixed launch velocity. © PASCO

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Summarise your learning for a projectile fired at an angle to the horizontal Direction of motion ForcesVelocityAcceleration Horizontal Vertical

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Direction of motion ForcesVelocityAcceleration Horizontal Air resistance negligible so no forces in the horizontal ConstantNone Vertical Air resistance negligible so only force of gravity acting in the vertical Changing with time Constant or uniform acceleration of – 9.8 m s –2 Summarise your learning for a projectile fired at an angle to the horizontal

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Summarise your learning for all projectiles! Direction of motion ForcesVelocityAcceleration Horizontal Vertical

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Projectiles at an angle to the horizontal Select a velocity and select an angle. Calculate the horizontal and vertical components Will the projectile hit the target? Other resources assMechanics/Projectile/Projectile.swf

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A thought experiment… remember our death- defying motorcyclist?

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What would happen if the building were taller? And the horizontal velocity greater?

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And if the Earths surface curved away more steeply?

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This is what Newton thought about, sometime between 1643 and

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This is taken inside an aircraft. Explain why these NASA trainee astronauts (class of 2004) appear weightless. © NASA

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Watch the clip on microgravity © NASA

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Group challenge! Complete the Weightless Wonder task to apply your understanding of equations of motion to a real situation. _Through_Algebra_Weightless_Wonder.html © NASA

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What is gravity? What is the force of gravity? What are the effects of gravity? What do we know about gravity? How can we make use of gravity?

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Investigating the force of gravity on Earth Using classroom resources, investigate how you could measure the gravitational field strength on Earth. What are you measuring? How are you measuring it? What does it mean? © NASA

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Uncertainties in your results © NASA

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What do the results mean? What have you measured? © NASA

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Can you measure gravitational field strength directly? © NASA

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Making use of the force of gravity Newtons thought experiment of 300 years ago became a reality on 4 October The Soviet Union (USSR) successfully launched the worlds first artificial satellite, Sputnik 1.

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Researching physics What was the significance of Sputniks launch, more than 50 years ago? What impact has the space race and our ability to launch satellites into space had on life on Earth?

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Topics for researching The historical aspects of the space race and its significance to humankind. Low orbit and geostationary satellites. Satellite communication and surveying. Environmental monitoring of the conditions of the atmosphere.

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Scientific communication and criteria for assessment Another opportunity to build skills for researching physics units. Insert more information once released! Quality sources for research. Communication of understanding, including summarising information in own words. Scientific content within communication.

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Reviewing our learning In this section, we have developed our understanding of motion to build from vertical projectiles, to horizontal projectiles and projectiles at an angle. We have followed the thought processes of Sir Isaac Newton through to the very first successful launch of a satellite, and considered how scientific developments impact on life on Earth.

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A final thought… This paragraph is taken from an article about a sample of wood being taken on a NASA mission to orbit Earth. A piece of Sir Isaac Newton's apple tree will defy gravity, the theory it inspired, when it is carried into space on the next Nasa shuttle mission. © BBC News website Discuss!

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