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Projectile Motion

Notes and Explanations

Some diagrams and simulations from

www.physicsclassroom.com

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What is a Projectile?

Anything that is thrown or shot through

the air.

Projectiles have velocities in two

directions.

Horizontal Motion: Motion parallel to the

Earths surface.

Vertical Motion: The force of gravity pullingdown on the object.

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Projectile Motion

A projectiles horizontal and vertical

motion are completely independent of

each other. Gravity will effect a projectile and a falling

object in the same way.

Therefore, if an object is dropped andthrown at the same time they will hit the

ground at the same time. It does not

matter that the projectile travels a farther

distance.

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Newtons Cannon

Newton described the possibletrajectories of a cannonball shot from atall mountain. Weaker shots fall inparabolas, but soon the curvature ofthe earth becomes more important. If

you could ignore air resistance,stronger shots would clear the horizon.If you could launch the cannonball fastenough, its curve would match thecurvature of the earth. This is called anorbit. A satellite is no more than aprojectile moving fast enough tocontinually clear the horizon as it falls.

Simulation of Newtons Cannon

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Curved Path

A projectile is any object that is projected

by some means and continues in motion

by its own inertia. Without gravity, the

object would follow a linearmotion; withgravity, the path curves.

The path is surprisingly simple if the

horizontal and vertical components ofmotion are investigated separately.

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HORIZONTAL COMPONENT:

If friction is ignored (and we always ignorefriction), then there are noforces acting onthe x-axis.

If net force is zero, then acceleration is zero. If acceleration is zero, then the object is either at

rest or moving at constant velocity. Since we know that the object is already in motion, the

projectile must be moving at constant speed on the x-

axis.

It moves of its own inertia and covers equaldistances in equal intervals of time.

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VERTICAL COMPONENT:

Projectiles move just like a freely falling

object along the y-axis.

The changing motion is due only to

acceleration due to gravity.

On the way up, the object decreases its

speed as it goes againstgravity.

On the way down, speed increases as itmoves withgravity.

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Vector Combination

The curved path of a projectile is acombinationof these horizontaland vertical components. Thecurved path of a ball (as shown inthe diagram) is best analyzed byconsidering the horizontal and

vertical components of motionseparately.

Note that the balls horizontalcomponent of motion doesntchange as the falling ball movesforward.

Note the vertical positions becomefartherapart with time and that thevertical distances traveled are thesameas if the ball were simplydropped.

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Projection Angles

With the same initial speed but different projection angles, a projectile willreach different altitudes(height above the ground) and different ranges(distances traveled horizontally).

However, the same range can be obtained from two different angles,symmetrically around a maximum of 45, as shown in the graph.

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Symmetry

The path of a projectile is symmetrical

It rises to its maximum height in the same time it

takes to fall from that height to the ground.

Because acceleration is the same all of the time,the speed it loses while going up is the same as

the speed it gains while falling.

Therefore the speeds are the same at equaldistances from the maximum height, where the

vertical speed is zero.

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Questions:

At the instant a horizontally held rifle is fired over level ground, abullet held at the side of the rifle is released and drops to theground. Ignoring air resistance, which bullet strikes the ground first?

A projectile is launched at an angle into the air. If air resistance isnegligible, what is the acceleration of its vertical component ofmotion? Of its horizontal component of motion?

At what part of its trajectory does a projectile have minimum speed? A ball tossed into the air undergoes acceleration while it follows a

parabolic path. When the sun is directly overhead, does the shadowof the ball across the field also accelerate?

Draw a free body diagram of a projectile.

What type of motion occurs on the horizontal axis? How in the world can object be moving upward if the only forceacting upon it is gravity?

Are horizontal forces required to keep the projectile movinghorizontally?

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Answers

They strike at the same time.

-9.8 m/s2; 0

At maximum height.

NO!

Should show weight only.

Constant

Inertia

NO!

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Memorize the following conceptual

notions about projectiles:

a projectile is any object upon which the only force is gravity,

projectiles travel with a parabolic trajectory due to the influence ofgravity,

there are no horizontal forces acting upon projectiles and thus no

horizontal acceleration, the horizontal velocity of a projectile is constant (never changing invalue),

there is a vertical acceleration caused by gravity; its value is ~10m/s2, down,

the vertical velocity of a projectile changes by ~10 m/s each second,

the horizontal motion of a projectile is independent of its verticalmotion.

the speed of a projectile is symmetrical around its maximum height.

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Use these sites to answer the

questions on the next slide.

Simulation #1

Simulation #2

Simulation #3

Simulation #4

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Questions

What launch angle maximizes the range (horizontal distance)?

What launch angle maximizes the height reached?

How does the time spent in the air depend on the launch angle?

Compare what happens at one angle, and then at 90 degrees minusthat angle (30 and 60, for instance).

What does Newtons Cannon show?

What happens to the trajectory when the mass of the projectile ischanged?

What effect does air resistance have on a trajectory?

What happens to the trajectory when the initial velocity is changed?

What conditions must exist so that two projectiles will collide inmidair? What effect do the initial velocities, height differences, and

angles have on this collision? Compare the trajectories of a projectile that is under the influence of

gravity and one that is not?