10 Projectile Motion Projectile Launched Horizontally Projectiles Launched at an Angle Hang time Revisited Fast-Moving Projectiles—Satellites Circular Satellite Orbits Elliptical Orbits Kepler’s Laws of Planetary Motion Energy Conservation and Satellite Motion

Horizontal motion does not affect gravity! Each ball has same initial vertical velocity Each ball’s vertical acceleration is same. Each ball hits at the same time

Two component look at projectile motion

Force and Projectile Motion Horizontal force is zero – Horizontal velocity constant. Vertical force is weight – Vertical velocity is decreasing.

Each component affects range vertical component affects time of flight Range = (horizontal component) x (time of flight) as angle increases (time of flight) increases as angle increases (horizontal component) decreases

Range Variation when initial and final height of projectile is same when air resistance is negligible

Air Resistance Effect

Distance of Fall d = ½ gt2 with g = 10m/s/s t = 1s d = 5m

Another way to see “distance of fall” in projectile motion

Satellite Motion

Kepler’s Laws