Projectile Motion

Projectile MotionProjectile Motion

Today’s Objectives:Recognize examples of projectile motion, Recognize that the horizontal and vertical components of a projectile’s motion are independent of each other, andResolve vectors into their components, and apply the kinematic equations to solve problems involving projectiles.

What Is Projectile What Is Projectile Motion?Motion?Projectile Motion is the motion of objects moving in two dimensions under the influence of gravity. Air resistance is negligible (we can ignore it).

EXAMPLES OF PROJECTILESExamples of projectiles include

anything launched or thrown into the air such as cannon balls, baseballs, pumpkins, soccer balls, tennis balls, handballs, racquetballs, people, four-square balls, softballs, mothballs, fireworks, water from rain clouds or from a hose…

There Are Some There Are Some Common Common Misconceptions….Misconceptions….

Going fast horizontally means you don’t fall as fast.

If you go fast enough, you don’t fall at all.

Gravity won’t act on you until you look down.

The Truth The Truth Is...Is...

If gravity is the only force acting on an object, it will accelerate at a rate of 9.8 m/s2 DOWN, regardless of what’s happening horizontally.

In fact, if the object doesn’t have wings, jet engines, propellers or rockets, its horizontal motion will have absolutely no effect on its vertical motion.

They are completely They are completely independentindependent of of each other.each other.

This is Key……To understanding projectiles:Horizontally, projectiles move

with constant velocity.Vertically, projectiles move with

constant acceleration.

WHY? Lets Consider a Little WHY? Lets Consider a Little Information About… Newton’s Laws Information About… Newton’s Laws of Motionof Motion

Newton’s First Law of Motion, also known as the Law of Inertia, states that a body in motion will remain in motion at constant velocity, unless acted upon by an unbalanced force (and that a body at rest will remain at rest).

Therefore, if there were no gravity, an object fired from a cannon off a hilltop would continue along a straight-line path at constant velocity forever and ever…the horizontal motion remains constant.

The Path of a Projectile… Without The Path of a Projectile… Without GravityGravity

The cannon ball moves a constant amount with each second.

Path of a Projectile… With Path of a Projectile… With GravityGravity

221

i gttvy y

WATCH THE NUMBERS

The Horizontal Motion is The Horizontal Motion is Independent of the Vertical Independent of the Vertical MotionMotion

HORIZONTAL VELOCITY is STILL Constant

WHAT DOES THE PILOT SEE (LOOKING DOWN)IF THE PLANE WERE MADE OF GLASS ?

What’s a Satellite??

Consider Horizontal and Vertical Consider Horizontal and Vertical Components of Motion Components of Motion IndependentlyIndependently

Vertical Components:y - vertical displacementg - vertical acceleration (9.8 m/s2)vyi - initial vertical velocity

vyf - final vertical velocity

t - time

Horizontal Components: x - horizontal

displacementvxi = vxf - horizontal velocity

t - time

How Do We Solve Projectile Problems??How Do We Solve Projectile Problems??

Vertical Equationsvf = vi + at vyf = vyi - gt

vf2 = vi

2 + 2a y vyf2 = vyi

2 - 2g y

y = vit + 1/2at2 y = vyit – 1/2gt2

y = 1/2(vi+vf)t y = 1/2(vyi+vyf)t

y = vft - 1/2at2 y = vit + 1/2gt2Horizontal Equationx = vxt

How Do We Solve Projectile How Do We Solve Projectile Problems??Problems??

These equations assume that down is negative!!

Since horizontal acceleration is zero, this is the only equation.

1. Draw an accurate diagram showing the trajectory of the object.

2. Solve for the horizontal and vertical components of the initial velocity, if given.

3. Complete a data table using given and implied data, based on an appropriate sign convention (you assign).

4. Identify what you are looking for. Remember you need at least 3 pieces of vertical data to use kinematic equations… if you don’t have 3, look to the horizontal data to find time, which is the only common variable.

How Do We Solve Projectile How Do We Solve Projectile Problems??Problems??

‘Human’ CannonballMr. Maroo is launched from a cannon with an initial velocity of 18 m/s at an angle of 25° with the horizontal. (a) How high will he go? (b) Where should a safety net be placed so that he lands safely? (c) How much time does he spend in the air?

Given: Vi=18 m/s

Vxi=18 m/s cos 25°= 16.3 m/s

Vyi=18 m/s sin 25°= 7.6 m/s

V H

25°

Vyi=7.6 m/s Vxi=16.3 m/sg=-9.8 m/s2

Vyf= 0 m/s

Practice With an Applet

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/ProjectileMotion/jarapplet.html