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Unit 3. Motion in Two Dimensions EQ: What is a projectile?. Projectile Motion. A projectile is an object that is shot through the air. Three types of projectiles: Projectiles shot vertically (90 degrees) Projectiles shot horizontally (0 degrees)
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Unit 3 Motion in Two Dimensions EQ: What is a projectile?
Projectile Motion • A projectile is an object that is shot through the air. Three types of projectiles: • Projectiles shot vertically (90 degrees) • Projectiles shot horizontally (0 degrees) • Projectiles shot at some angle between 0-90 degrees
Projectiles • The path that a projectile takes while in flight is called the trajectory. The shape of this path is called a parabolic curve (or parabola). • The horizontal distance that the projectile travels is called its range or displacement. • The highest point in the trajectory is called the maximum height.
Diagram of an Angled Projectile dy-max Time up equals time down dx
Hangtime • The time a projectile spends in the air is called its hangtime. • If shot horizontally, there is no “up” time, it is all time down. • If shot at any angle greater than 0 degrees, the projectile will travel up for a while, then down. The time up is equal to the time down. • The closer the launch angle is to 90 degrees, the more time the projectile will spend in the air (assuming that the initial velocity is constant).
vx dy t dx Diagram of Horizontal Projectile vx= horizontal velocity dy= vertical height t= time to fall dx= final displacement
Projectile Motion Facts • Horizontal (x) and Vertical (y) components are independent of each other • No force acts horizontally; Horizontal motion is constant. • Force of gravity acts vertically; vertical motion is accelerated
Horizontal Projectile formulas • The horizontal velocity of a projectile does not change while in flight. we know that ax = 0 This means we have constant velocity So we can use this to find distance
Horizontal Projectile formulas • To find the time of flight for a horizontal projectile, you need to know how high it was dropped from then solve for t: we know that Vi = 0 So the time will only depend on how high the object is and the acceleration due to gravity
Horizontal Projectile Formulas • To find the vertical velocity of a projectile that was initially shot horizontally, you will need to know the time that it was in the air: we know that Vi = 0 So the time will only depend on the time it was accelerated by to gravity
Example 1 • A ball is thrown from the top of a 125m tall structure with an initial horizontal velocity of 15m/s. • How long will it take for it to hit the ground? • How far will it land from the base of the structure? • What was the vertical component of the velocity immediately before the ball hit the ground?
Example 2 • An arrow is shot horizontally from 2.0m above the ground and lands 75m away from the shooter. • How long was it in the air? • What was the initial speed of the arrow?
Horizontal Projectile formulas • The horizontal velocity of a projectile does not change while in flight. begin with: we know that ax = 0 After simplifying we end up with:
Horizontal Projectile formulas • To find the time of flight for a horizontal projectile, you need to know how high it was dropped from then solve for t: begin with: we know that: Vy=0 for horizontal flight ay=g (acceleration due to gravity) After simplifying we end up with:
Horizontal Projectile Formulas • To find the vertical velocity of a projectile that was initially shot horizontally, you will need to know the time that it was in the air: begin with: we know that: Viy=0 for horizontal flight ay=g (acceleration due to gravity) After simplifying we end up with:
