Projectile Motion

Motion In Two Dimensions

We restrict ourselves to objects thrown near the Earth’s surface so that gravity

can be considered constant.

Objectives

1. For a projectile, describe the changes in the

horizontal and vertical components of its velocity,

when air resistance is negligible.

2. Explain why a projectile moves equal distances

horizontally in equal time intervals when air

resistance is negligible.

3. Describe satellites as fast moving projectiles.

Projectile motion applies to sports.

Projectile motion applies to destructive

projectiles.

A projectile is any object that moves through

the air or through space, acted on only by

gravity (and air resistance).

The motion of a projectile is determined only

by the object’s initial velocity, launch angle and

gravity.

Projectile motion is a combination of horizontal

motion and vertical motion.

The horizontal motion of a projectile is constant

because no gravitational force acts horizontally

The vertical motion of a projected object is

independent of its horizontal motion.

Let's say a Wiley coyote runs off a cliff. As he

leaves the cliff he has a horizontal velocity.

As soon as the coyote leaves the cliff he will

experience a vertical force due to gravity.

This force will cause him to start to accelerate

in the vertical direction.

As he falls he will be going faster and faster in

the vertical direction

In a lot of books you will see the horizontal component

called x and the vertical component called y.

The horizontal and

vertical components of

the motion of an object

going off a cliff are

separate from each other,

and can not affect each

other.

X

Y

The x-component of a projectile’s

motion is there from the start, and

stays the same the entire time.

The y-component

of a projectile’s

motion doesn’t

even exist at the

beginning, but

grows bigger as

the object falls.

The vertical motion of a projectile is nothing more than

free fall with a constant downward acceleration due

to gravity.

A projectile, once projected, continues in

motion by its own inertia and is influenced

only by the downward force of gravity.

Gravity accelerates objects downwards, but is

unable to affect the horizontal motion of a

projectile.

A projectile moves horizontally with constant

velocity while being accelerated vertically. The

result is a motion in a curved path.

The path of a projectile is called its trajectory.

The trajectory of a projectile in free fall is a parabola.

The total

distance

traveled by a

projectile is

known as its

range.

Horizontal Shot.

If the barrel of a rifle is horizontal to the surface of

the earth when fired, the bullet never rises above

the barrel, and gravity causes an immediate

descent.

Projectile Vectors

Horizontal and vertical components are represented as

vectors.

An object projected

horizontally will

reach the ground in

the same time as

an object dropped

vertically.

No matter how

large the horizontal

velocity is, the

downward pull of

gravity is always

the same.

The cannonball falls the same amount of distance as it did

when it was merely dropped from rest

Horizontal

Motion

Vertical

Motion

Forces

PresentNo Yes

Gravity acting downward

Acceleration

Present

No Yes

Gravity downward at

approx. 10 m/s2

Velocity Constant Changing

(by approx. 10 m/s each

second)

Projectile Motion Summary

Horizontally launched projectile

Horizontal velocity is constant. Vertical velocity is changing

due to gravitational acceleration..

Vertically launched projectile

The horizontal velocity component remains the same size

throughout the entire motion of the cannonball.

If projectiles are launched at the same speed, but at different

angles, the height and range is of the projectile are affected.

The same range can be reached by two different angles.

90 minus the first angle will give you the second of the same range.

Ex: 90-30=60. 90-75=15.

Sports Trivia

Maximum range is achieved if the projectile is

fired at an angle of 45 degrees with respect to

the horizontal.

0°, 90°minimum range

45°maximum range

Angle with Longest time in Air? 90°

Which angle of projection causes a projectile to stay in the air longer? 50 or 70 degrees

70 degrees,

(closest to 90, longer time in air)

If it takes 4 seconds for a projectile to rise to its peak, then

it takes 8 seconds to move through the air from start to

finish. Why?

Because the vertical

velocity changes by approx.

10 m/s (in the upward or

downward direction) each

second.

For example

If a projectile is moving

upwards with a velocity

of 40 m/s at 0 seconds,

then its velocity will be:

30 m/s after 1 second

20 m/s after 2 seconds,

10 m/s after 3 seconds,

40 m/s after 8 seconds.

Free Fall Results

• Horizontal motion is constant

• Vertical Motion is accelerated

• Rise time = Fall Time

• Final speed = Initial speed

When the effect of air resistance is significant,

the range of a projectile is diminished and the

path is not a true parabola.

In Conclusion

A projectile is any object upon which the only force

is gravity.

Projectiles travel with a parabolic trajectory due to

the influence of gravity.

There are no horizontal forces acting upon projectiles

and thus no horizontal acceleration.

The horizontal velocity of a projectile is constant.

there is a vertical acceleration caused by gravity

(approx. 10 m/s).

The horizontal motion of a projectile is independent

of its vertical motion.

Test your knowledge

Suppose a truck is equipped with a

flare launcher which is capable of launching

a sphere vertically. If the truck is in

motion and launches the flare and maintains a

constant horizontal velocity after the launch,

then where will the flare land (neglect air

resistance)?

Test your knowledge

Suppose an airplane drops a flare while it

is moving at constant horizontal speed at

an elevated height. Assuming that air

resistance is negligible, where will the flare

land relative to the plane?

A. Directly below the plane.

B. Below the plane and ahead of it.

C. Below plane and behind it.

Why does the horizontal component of a

projectile’s motion remain constant?

Because no force acts on it horizontally.

Why does the vertical component of a

projectile’s motion undergo change?

Because gravity is pulling it downward.

How does the vertical distance a projectile

falls below an otherwise straight-line path

compare with the vertical distance it would

fall from rest in the same time?

The vertical and horizontal distances are

equal.

A projectile is launched vertically at 100

m/s. If air resistance can be neglected, at

what speed does it return to its initial

level?

100 m/s

A rock is thrown upward at an angle.

What happens to the horizontal

component of its velocity as it rises?

(Neglect air resistance.)

(a) it decreases

(b) it increases

(c) it remains the same(c) it remains the same

A horizontally traveling car drives off of a

cliff next to the ocean. At the same time

that the car leaves the cliff a bystander

drops his camera. Which hits the ocean

first? (Neglect air resistance.)

(a) car

(b) camera

(c) they both hit at the same time(c) they both hit at the same time

When a rifle is being aimed at a distant

target, the barrel should be lined up so that

it points:

A. Slightly higher than the target

B. Exactly at the target

C. Slightly lower than the target