What is Projectile Motion?

Projectile Motion Two-dimensional motion of an object Vertical Horizontal

Projectiles Airborne objects that move as a result of their own inertia and gravity. They exhibit two dimensional motion. Horizontal and vertical motion Horizontal and vertical motion are independent of one another. The resultant motion is a combination of horizontal and vertical motion.

Types of Projectile Motion Horizontal Motion of a ball rolling freely along a level surface Horizontal velocity is ALWAYS constant Vertical Motion of a freely falling object Acceleration due to gravity Vertical component of velocity changes with time Parabolic Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

Components of Projectile Motion Projectiles have: vertical velocities that increase and decrease because they are influenced by gravitational forces. horizontal velocities remain constant because they are not influenced by gravitational forces.

Examples of Projectile Motion Launching a Cannon ball

Two Dimensional Horizontal Motion for Projectiles Horizontal displacement “x” is called the range. d = v1t x = vt Assume v1 does NOT change. So v1 = v2 therefore the acceleration in the x or horizontal direction is always zero.

Two Dimensional Vertical Motion for Projectiles Displacement in the “y” is called the height. Assume the acceleration is -9.8 m/s2 Assume v1 is zero d=1/2 at2 y = ½ at2 V22 = 2ad V22 = 2ay V2 = at V2 = at

Factors Affecting Projectile Motion What two factors would affect projectile motion? Angle Initial velocity Initial Velocity Angle

Class Exercise An object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontal Calculate the horizontal and vertical components of the initial velocity After 2.0 seconds, how far has the object traveled in the horizontal direction? How high is the object at this point?

Solution Part a Part b Part c

Two Types of Projectiles

Steps to working a problem Draw the picture Label with variables and numbers Write the givens Write what you are looking for Write equation Plug and chug Answer with number and unit!

Anytime an object starts at an angle from the ground! Vy at the highest peak is always 0 Remember when use max height and Vy=0….it’s only half the time the object stays in the air So…to find total distance (dx)…multiply time by 2

Anytime the object starts at a given height Do not multiply time by 2….since starts at max height already

A. Maximum height of projectile B. Launch Velocity C. Launch angle EX 1: A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … … note – think of various ways this question could be formed on a test (cannon fires, football thrown, baseball hit, golf ball hit, soccer ball kicked, etc.) A. Maximum height of projectile B. Launch Velocity C. Launch angle

A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … A. Maximum height of projectile. Answer … Begin with equation Use the fact that at top of trajectory Vyi is zero. And use second half of trajectory. Formula simplifies to Plugging in values:

A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … B. Launch Velocity. Answer … Need X and Y velocities (Vavg.x and Viy). Launch velocity is found using Pythagorean theorem. Vx is found using: Viy is found using half of trajectory and: Knowing that Vfy is zero at half the time … So …

Use triangle and trig function. So A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … C. Launch Angle. Answer … Use triangle and trig function. So θ

Ex 2:An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … … note – think of various ways this question could be applied (dropped from a moving vehicle, dropped by a flying object, rolls off a cliff, rolls off a table, etc.) A. Velocity of object

An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … A. Velocity of object. Answer: Typical to these types of problems, first step would be to find the time in the air (fall time). This is found using the vertical distance (dy).

An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … Velocity of object. Answer: Then use time (8.45 s) with X distance (dx) to calculate horizontal velocity (Vx).

Ex 3: An object is travelling at 37◦ with an initial velocity 8 m/s Ex 3: An object is travelling at 37◦ with an initial velocity 8 m/s. How long will it take to go 38 m horizontally? … note – think of various ways this question could be applied (boat/swimmer crossing river, airplane, ball thrown from vehicle, etc..)

Need X component velocity. Answer: An object is travelling at 37◦ from vertical at velocity 8 m/s. How long will it take to go 38 m horizontally? Need X component velocity. Answer: Note that (similar to projectiles) time is shared between two motions. Each component is independent of the other. θ=37

Review Questions In the absence of gravitational force and friction, describe the motion of an object. How do you describe horizontal motion? Is vertical motion influenced by gravitational force? How far is an object being thrown horizontally given an initial speed of 20 m/s from a 45 m tower?