By Allison Appleby For Physics References: Pearson Aust (2010) In2Physics Shadwick, B (2003) Surfing Physics: Space. Science Press Andriessen et al (2008) Physics 2 HSC course; 3 rd edition. John Wiley and Sons Aus Ltd

Projectile Motion Ideas through time Before Galileo- ideas of Aristotle: horizontal motion and then vertical drop Definition Ballistic Trajectory= the path of an object through the air (subject only to gravity and air resistance)

Projectile Motion Ideas through time After Galileo- projectile path is part of a parabola with separate horizontal and vertical components (VECTORS) Horizontal motion is constant velocity Vertical motion is accelerating (g)Definition Ballistic Trajectory= the path of an object through the air (subject only to gravity and air resistance)

Projectile Motion Ideas through time When these components are put together we get parabolic motion

Projectile Motion Ideas through time The motion of an object depends on the FRAME OF REFERENCE The motion of the object from a viewer at a distance A person running with the object would only see the vertical component of motion

Remember from preliminary physics: The motion of a moving object relative to another moving object: v B = v B -v A This is also called the Galilean Transformation Example Car A is travelling at 100km/hr. Car B is travelling at 80 km/hr in the same direction. What is the velocity of car A compared to car B? 20km/hr Click for answer

Ideal parabolic trajectory Air resistance must be negligible Height and range of motion is small enough that the curvature of the earth can be ignored Vertical component is the y axis- acceleration due to gravity a y =g ↑ is the positive direction ↓ is the negative direction As gravity is down a y = m/s 2 Horizontal component is the x axis- velocity is constant a x =0 → is the positive direction ← is the negative direction

Properties of ideal parabolic trajectories At maximum height v y =0 Trajectory is horizontally symmetrical about the maximum height It takes the same time to reach maximum height as it does to fall back to the original height Initial speed= final speed (on horizontal ground) Maximum height is reached at 90 o launch angle and maximum range is reached at 45 o launch angle All objects projected horizontally from the same height have the same time of flight as one dropped from rest at the same height (initial vertical velocity = 0)

Solving Projectile Motion Problems We use SUVAT equations from preliminary physics: s = r = displacement = Δx = x f = x i = Δy = y f – y i SOHCAHTOA v=s/t or v av = Δ r / Δ t a av = v-u t SUVAT (straight line motion) Horizontal component Vertical component u x =ucosΘu y =usinΘ v = u + atv x =u x (a x =0)v y =u y + a y t v 2 =u 2 + 2asv x 2 =u x 2 v y 2 =u y 2 + 2a y Δy s= ut + ½ at 2 Δx = u x tΔy = u y t + ½ a y t