Projectile Motion

Projectile Motion

Motion in Two Dimensions

Poll

At the instant a horizontally pointed cannon ball is fired, a cannonball held at the cannon’s side is released and drops to the ground.  Which cannonball strikes the ground first?

• the one fired from the cannon

• the one dropped

• they hit the same time

What is a Projectile?

Any object that continues in motion by its own inertia and is influenced only by the downward force of gravity (and air resistance)

- an object dropped from rest is a projectile

- an object thrown straight upward is a projectile

- an object thrown upward at an angle to the horizontal

The path that the projectile
follows is a parabola…

the path is called its trajectory

Multiple Choice

What shape is the path of a projectile?

• hyperbola

• circle

• parabola

• triangle

Horizontal Motion

 If there is no force acting on an object, then it will continue

moving at a constant speed in the same direction.

- there will be no change in its velocity

- distance will increase the same amount with each second

Free Fall Revisited

 An object in free fall is only acted on by gravity

- Acceleration due to gravity is 9.8 m/s²

– distance covered increases with each second

Projectile Motion Combines Vertical
Motion and Horizontal Motion

 The vertical motion of a projectile is not affected

by its horizontal motion

-meaning: The vertical motion of a projectile is

identical to an object in free fall

 The horizontal motion of a projectile is not

affected by its vertical motion

- meaning the projectile will travel the same

horizontal distance as it would if it were simply
rolling on a flat surface in the absence of
friction

Projectile Motion Combines Horizontal Motion and Vertical Motion

The vertical and horizontal motion of a projectile are independent of each other

​

Projectile Motion Combines Horizontal Motion and Vertical Motion

The vertical and horizontal motion of a projectile are independent of each other

​

Projectile Motion Combines Horizontal Motion and Vertical Motion

The vertical and horizontal motion of a projectile are
independent of each other

​

Projectile Motion Combines Horizontal Motion and Vertical Motion

The vertical and horizontal motion of a projectile are independent of each other

​

Projectile Motion Combines Horizontal Motion and Vertical Motion

The vertical and horizontal motion of a projectile are
independent of each other

Horizontal Path Without Gravity

Vertical Path

Projectile Motion

 Projectiles follow a parabolic

trajectory
 Horizontal component along

trajectory remains
unchanged.

 Acceleration only occurs in

the vertical component

Make sure to note: at the very top of the arc, the v_y is 0!

Projectile Motion and
Complementary Angles

 Different launch angles result in different

horizontal distances traveled by the projectile

 Same range is obtained from two different launching angles

when the angles add up to 90°.

 Object launched at an angle of 60 has the same range as if it

were thrown at an angle of 30.

Multiple Choice

What launch angle would have the same range as a projectile launched at 20°?

• 90

• 70

• 60

• 80

Projectile Calculations

Horizontal Distance
d = v(t)

Vertical Velocity
Vf = Vi + gt

For Projectiles Launched horizontally

Horizontal Velocity
vf = vi + at

Vertical Distance
d = vit + ½ gt2

Multiple Choice

Is projectile motion one dimensional?

• yes it's one dimensional

• no it's two dimensional

• no it's three dimensional

Multiple Choice

Which direction, horizontal or vertical has acceleration?

• horizontal

• vertical

Multiple Choice

Which direction, horizontal or vertical has constant speed?

• horizontal

• vertical

Open Ended

Two identical balls roll off the edge of a table.  One leaves the table traveling twice the speed of the other.  Which ball hits the floor first? Explain why.

Review

 At the instant a horizontally pointed

cannon ball is fired, a cannonball held at
the cannon’s side is released and drops
to the ground. Which cannonball strikes
the ground first, the one fired from the
cannon or the one dropped?

 They hit at the exact same time

Draw

Draw vector arrows representing the v_x and v_y velocity components during the course of the motion. The length of the arrows should represent the magnitude of the velocity components.

Draw

Draw vector arrows representing the v_x and v_y velocity components during the course of the motion.

Multiple Choice

At what point is v_y= 0 m/s?

• A

• B

• C

• D

• None of these points

Multiple Choice

At what point is v_x= 0 m/s?

• A

• B

• C

• D

• None of these points

Multiple Choice

A vector is a quantity that has

• magnitude and time
• time and direction
• magnitude and direction
• direction and rhythm 

Multiple Choice

Which of the following would NOT be considered a projectile? 

• a cannonball thrown straight up
• a cannon ball rolling down a slope
• a cannonball rolling off a table
• a cannonball thrown in the air

Multiple Choice

The horizontal component of a projectile's velocity is independent of...

• it's range
• time
• the vertical component
• none of these

Multiple Choice

What is the horizontal acceleration of a projectile?

• 0 m/s²
• -9.8 m/s²