Projectile Motion

2015

What is projectile motion?

• Any object that moves through air or space• is a form of two-dimensional motion that

deals with the motion of objects under the influence of gravity.

There is motion in both the horizontal plane (x-axis) and the vertical plane (y-axis).

Projectile motion• The path in which a projectile travels is a

parabolic curve so long as there is no wind resistance.

WEEE……

Projectile motion problems are best solved bytreating horizontal and vertical motion separately.

*IMPORTANT*Gravity only affects vertical motion.

There are two main typesof projectile motion situations.

1. object launched horizontally2. object launched at an angle

Horizontal Motion:

If there is no gravity, an object moving horizontally (in the x-direction) would continue to move in a straight line.

Vertical Motion

If an object is dropped vertically (in the y-direction), the gravity causes it to

accelerate downwards.

Projectile motion

Projectile motion is a combination! In the x-direction, it continues to move at a constant

speed, but in the y-direction, it accelerate downward because of gravity!

Remember this!!!!!!!!!!!

For a projectile: THE X-VELOCITY IS independent of the Y-VELOCITY!!! The speed

in the x-direction doesn’t care about what the speed in the

y-direction is!

Why?Remember that gravity is

only pulling in one direction down and

nothing is pulling right or left. If there is no

gravity, a projectile would go straight

forever.

Velocity Vectors

Remember that velocity has a direction, so it can be represented using vectors! We can break down the velocity into separate x- and y-

components.

Velocity Vectors

Let’s examine the x and y velocity vectors for a projectile:

Its x-velocity stays constant and its y-velocity increases.

Y-Velocity

Just like in freefall: Velocity in the y-direction decreases on the way up, and increases on the

way down. At the top of the path, the y-velocity is always

zero. Velocity on the way up equals velocity on the

way down when you reach the same height.

Question #1

If you were walking at a constant velocity with a baseball and threw it up into the air while you were walking, would it fall

a. in front of youb. behind youc. right back into your hands

Answer

• Its y-velocity is different than your, but its x-velocity stays the same as you. It should land back in your hands!

Question #2

An airplane is carrying a bomb and traveling with a velocity of 1,100 mph east. If it releases its bomb and continues at that velocity, will the bomb land

a. directly underneath the planeb. behind the planec. ahead of the plane

Answer

If they’re going at the same x-velocity, it will land directly beneath the plane!

Projectiles vs. Free Falling Objects

Projectiles fall at the same rate as free falling objects. They will hit at the

same time, because they are both being pulled by gravity at the same rate! Only one will have a

greater x-range.

Solving for projectile motion

• Since projectiles travel in both the horizontal and vertical planes, we can solve for the X and Y components.

We can use the one-dimensional motion equations to solve for variables involved in two-dimensional motion problems.

Horizontal Projectile Motion

School

Book

Boo….. I don’t like school books!!

A VERY TALL BUILDING

CRASH!!!

x

-y

Vy = (g)(Δt)Vy² = 2( g)(Δy)Δy = ½(g)(Δt)²Δx = (Vx,i)(Δt)

Horizontal Projectile Motion Formulas

Sample ProblemThe Royal Bridge in Colarado is 321 m above the Arkansas River. If you kick a rock horizontally off the bridge and it hits the water with a horizontal displacement of 45 m, what is the velocity at which the rock was kicked?

Δy = -321 m

g = 9.81 m/s²

ΔxΔx = 45 m

Δy = -½(g)(Δt)²

√-2(Δy)/g = Δt

8.1 s = ΔtΔx = (Vx,i)(Δt)Δx/Δt = Vx,i

+ 5.56 m/s = Vx,i