Projectile motionProjectile motion is a form of is a form of two-dimensional motion in two-dimensional motion in which a “projectile” is under which a “projectile” is under the influence of gravity.the influence of gravity.

There is motion in both the horizontal There is motion in both the horizontal plane plane

(x-axis) and the vertical plane (y-axis).(x-axis) and the vertical plane (y-axis).

What is projectile What is projectile motion?motion?

What is a projectile?What is a projectile?

ProjectilesProjectiles are objects that are objects that are launched into the air.are launched into the air.

Ex. balls, arrows, long Ex. balls, arrows, long jumpersjumpers

Projectile motionProjectile motion The path in which a projectile The path in which a projectile

travels is a parabolic curve travels is a parabolic curve (assuming there is no wind (assuming there is no wind resistance). resistance).

Projectiles vs. Free Falling ObjectsProjectiles vs. Free Falling Objects

Projectiles fall at the same Projectiles fall at the same rate as free falling objects.rate as free falling objects.

Solving for projectile Solving for projectile motionmotion

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

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

Projectile MotionProjectile Motion

x-Motionx-Motion y-motiony-motion VVavgavg =Δx/Δt Δy = =Δx/Δt Δy = ½½ (v (vi i ++ vvff) Δt) Δt

g = (vg = (vf f - v- vii) / Δt) / Δt

Δy = vΔy = vii Δt + ½ Δt + ½ gΔt²gΔt²

vvff² = v² = vii² + 2gΔy² + 2gΔy

The same equations we used in 1-D motion! The trick is to solve for “x” and “y” motion of 2-D moving objects independently!

Projectile MotionProjectile Motion

Two types of projectile motion Two types of projectile motion situations:situations:

1. Horizontally launched 1. Horizontally launched projectilesprojectiles

2. Projectiles launched at an angle2. Projectiles launched at an angle

Horizontal Projectile Horizontal Projectile MotionMotion

Physics

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

Δy = -321 m

g = -9.81 m/s²

ΔxΔx = 45.0 m

ΔΔy = ½(g)(y = ½(g)(ΔΔt)²t)²

√√2(Δ2(Δy)/g = y)/g = ΔΔtt

8.10 s = Δ8.10 s = ΔttΔΔx = (Vx = (Vx,ix,i)()(ΔΔt)t)

ΔΔx/x/ΔΔt = Vt = Vx,ix,i

5.56 m/s5.56 m/s = V = Vx,ix,i