Motion in Two Dimensions EQ: What is a projectile? 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).

Diagram of Horizontal Projectile dy dx vx t 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: