YEAR 2 PROJECTILES 17122021 Basics of Projectiles Practice

PROJECTILES DEFINITIONS AND ASSUMPTIONS A projectile is an object that has been projected into the air by a force. When modelling projectiles, we usually make the following assumptions: • The projectile is modelled as a particle. • The only force acting on the particle is gravity. 17/12/2021 2

PROJECTILES | RECAP QUESTIONS 17/12/2021 3

PROJECTILES | RECAP QUESTIONS (a) Vertically 17/12/2021 (b) Horizontally 4

PROJECTILES | RECAP QUESTIONS (a) Find the times at which the particle is 4 m above the ground. (b) Hence find the total time for which the particle is more than 4 m above the ground. 17/12/2021 5

PROJECTILES | RECAP QUESTIONS (a) Find the times at which the particle is 4 m above the ground. (b) Hence find the total time for which the particle more than 4 m above the ground. Vertically (a) (b) 17/12/2021 6

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS Find the distance between the start point and where the ball hits the ground. 17/12/2021 7

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS Find the distance travelled by the ball. Horizontally Vertically +ve 17/12/2021 8

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS Find the distance travelled by the ball. Horizontally 17/12/2021 9

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS Vertically Horizontally 17/12/2021 10

MAGNITUDE AND DIRECTION OF THE VELOCITY. 17/12/2021 The horizontal component of the velocity is constant. The vertical component of the velocity changes (due to gravity). The direction of travel is therefore constantly changing. (see the direction of the arrows on the diagram below) At the highest point, the particle is travelling horizontally (the vertical component is zero) 11

MAGNITUDE AND DIRECTION OF THE VELOCITY |EPP Find the magnitude and direction of the velocity with which the stone hits the sea. 17/12/2021 12

MAGNITUDE AND DIRECTION OF THE VELOCITY |EPP Horizontally Vertically 17/12/2021 13

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS 17/12/2021 (a) Find the greatest height reached by the particle. (c) Find the magnitude and direction of the velocity when the particle hits the ground. 14

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS (a) Find the greatest height reached by the particle. Vertically 17/12/2021 15

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS Horizontally 17/12/2021 16

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS (c) Find the speed of the particle and the angle between the direct of motion and the particle when the ball hits the ground. Horizontally 17/12/2021 17

PROJECTILES | FURTHER EXAMPLE-PROBLEM PAIRS (c) Find the speed of the particle and the angle between the direct of motion and the particle when the ball hits the ground. Vertically Horizontally 17/12/2021 18

PROJECTILES | EXAM QUESTION PRACTICE 17/12/2021 EXAM QUESTIONS | THE BASICS AQA M 1 June 2009 Q 6 (similar to previous example) AQA M 1 June 2006 Q 7 (slightly harder than previous question) AQA M 1 January 2011 Q 7 (a good starting point if you’re already confident with the examples) EXAM QUESTIONS | A BIT TOUGHER AQA M 1 January 2013 Q 8 AQA M 1 June 2012 Q 8 AQA M 1 January 2008 Q 7 AQA M 1 January 2006 Q 5 19

TRAJECTORY OF A PROJECTILE The equation of the trajectory shows the relationship between the horizontal and vertical distance travelled. (Think of this as the ‘path’ of the projectile). 17/12/2021 20

DERIVING THE EQUATION OF THE TRAJECTORY 17/12/2021 Find the equation of the trajectory. Horizontally Vertically Substitute (1) into (2): (1) (2) 21

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 22

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR Horizontally Vertically 17/12/2021 23

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 24

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR Horizontally Vertically 17/12/2021 25

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 26

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR Horizontally Vertically 17/12/2021 27

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 28

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 Why don’t the curves go through (12, 4)? Extension Can you reproduce this graph in Desmos using the equation of the trajectory? 29

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR 17/12/2021 30

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR Find the angle above the horizontal at which the ball is struck. Horizontally Vertically Solution continues on next page… 17/12/2021 31

EQUATION OF THE TRAJECTORY | EXAMPLE-PROBLEM PAIR Find the angle above the horizontal at which the ball is struck. 17/12/2021 32

EQUATION OF THE TRAJECTORY | EXERCISE 17/12/2021 EXERCISE 17 B | PAGE 365 -366 A|NSWERS P 560 -561 Q 1 -6 EXERCISE 17 A | PAGE 361 A | NSWERS P 560 Q 1 (a) (i) Q 4 SEE NEXT PAGE FOR CHALLENGE QUESTION… For further challenging projectiles questions, check out OCR M 2 past papers. 33

OCR M 2 JUNE 2018 Q 8 17/12/2021 34

OCR M 2 JUNE 2018 Q 8 (a) From O to A Vertically 17/12/2021 From A to B CLICK FOR HINT 1 Horizontally Vertically CLICK FOR HINT 2 CONSIDER VERTICAL AND HORIZONTAL COMPONENTS FROM A TO B. WRITE DOWN KNOWN SUVAT VALUES 35

OCR M 2 JUNE 2018 Q 8 CLICK FOR HINT 3 (b) 17/12/2021 36