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Teaching Topics: Projectiles in M1 Stephen Lee Abstract • Techniques and strategies for teaching Projectiles in M1 will be given in this session, along with useful examples to enable students to grasp the key concepts. Introduction Starter exercise • Projectiles is a topic that builds upon the basics of motion in one dimension What projectiles occur in ‘real’ life? • It is an application which many students find interesting, yet one with which they can get lost in the detail • Javelin, Darts, Archery, Football, Tennis, Golf and many, many more sports! • Non-sport examples: – Gun shot, canons, fireworks • Clear presentation and statements are key Assumptions Students need to know the assumptions that are made about the motion, namely: MEI M1 Specification PROJECTILES The motion of a projectile M1y Be able to formulate the equations of motion of a 1 projectile. 2 Know how to find the position and velocity at any time of a projectile, including the maximum height and range. • A projectile is a particle • It is not powered • The air has no effect on motion 3 Be able to find the initial velocity of a projectile given sufficient information. 4 Be able to eliminate time from the component equations that give the horizontal and vertical displacement in terms of time. 5 Be able to solve problems involving projectiles. • Drop two balls example! 1 Nice 1-dimension question Question solution (Past exam question) (i) At the maximum height v=0 (ii) Find displacement for particle 1 after time t Find displacement for particle 2 after time t Then EITHER: Equate displacements and solve for t OR Sub in the given value for t to show the displacement is the same Starter for 2-D Starter for 2-D • Throw a (soft? juggling?) ball between students Points to try and draw out from the exercise Ask questions: • What shape is the trajectory? • How can you vary this? • How/why does the ball ‘get going’? • What happens to it once it leaves your hand? • What forces act upon it once in flight? • Shape is parabolic, but is dependent upon the initial speed and angle of the throw • You have to give the ball the initial ‘impetus’ but then it acts ‘freely’ • Once ‘in motion’ need to get students to see that there is no other force than gravity acting 2-D Projectiles 2-D Projectiles • The velocity of a projectile is split into two components, horizontal and vertical. This is the standard way to solve projectiles questions. • The equations of motion are then applied to each component of velocity. The main ones used are:- 2 Time of flight: Range and Max height: Projectiles Solution strategy Solution strategy Part (iv) direction of motion 3 Why is the path of a projectile parabolic? Solution strategy y 20ms-1 Assume g = 10 ms-2 60o x Displacement and velocity components: initial velocity Horizontal + component 20cos60o acceleration velocity at time, t (v=u+at) displacement at time, t (s=ut+at2/2) 0 20cos60o Vertical component + 20sin60o -10 20sin60o- x = 20t cos 60 10t t= 20tcos60o 20tsin60o- 5t2 x 20 cos 60 y = 20t sin 60 − 5t 2 x x ⎛ ⎞ ⎛ ⎞ y = 20 ⎜ ⎟ sin 60 − 5 ⎜ ⎟ ⎝ 20 cos 60 ⎠ ⎝ 20 cos 60 ⎠ x ⎛ ⎞ y = x tan 60 − 5 ⎜ ⎟ ⎝ 20 cos 60 ⎠ 2 2 Simulations Overview Key • Autograph examples • The force that initiates motion is a contact force. Once the motion of the ball is initiated, the role of contact force is over. It does not subsequently affect or change the velocity of the ball as the contact is lost. • Geogebra train example • Geogebra past paper (see ICT session 6b) • Geogebra golf cliff shot investigation (See Stretching B2) • Remember that RESULTANT FORCE is therefore only the particle’s weight (mass x gravity) NOT what is actually its velocity! • Draw a diagram if you are considering what the velocity is at a given time 4 Key • Need to make the distinction with the object’s velocity at a given time, i.e. horiz constant, vertical changing, hence resultant changes. • Check whether a projectile starts and lands at the same vertical height! 5