AIM: How can we describe the path of an object fired horizontally from a height above the ground? DO NOW: A ball rolls off a table top with an initial.

• AIM: How can we describe the path of an object fired horizontally from a height above the ground?

• DO NOW: A ball rolls off a table top with an initial horizontal velocity.

– Predict and draw the path that the ball will follow.

PHYSICS MR. BALDWIN

Projectile Motion October 24, 2013

PROJECTILE MOTIONHOW WOULD YOU DESCRIBE A PROJECTILE?

•A projectile is an object fired either above the ground horizontally or at an angle

with respect to the horizontal OR from the ground at an angle with respect to the

horizontal.

HOW WOULD YOU DESCRIBE THE PATH OF A PROJECTILE?

•The path of a projectile is always a PARABOLA.

WHAT FORCE(S) IS/ARE ACTING ON THE PROJECTILE?

•The only force (influence) acting on a projectile is GRAVITY.

THEREFORE, WHAT DO YOU THINK IS THE ACCELERATION OF

THE PROJECTILE?

•Its only acceleration is the ACCELERATION DUE TO GRAVITY, g

(9.80m/s2) always acting downwards.

CAN YOU NOW DEFINE A PROJECTILE IN ONE CONCISE SENTENCE?

A projectile is an object

moving in two dimensions

under the influence of the

Earth's gravity alone and

following a parabolic path.

It can be understood by analyzing the horizontal and vertical motions separately.

CHECK

Looking at the diagram, analyze the horizontal and vertical velocities of the projectile separately.

What did you observe?

• About the velocity in the x-direction?• The velocity in the x-direction is constant (never changes).• What does that imply?• The horizontal motion is uniform/constant.• About the velocity in the y-direction?• The velocity in the y-direction is increasing.• What does that imply?• The object is being accelerated downwards.• The object is falling with a constant acceleration g.

AIM: How can we describe the path of an object fired at an angle w.r.t. the horizontal? DO NOW: A ball is projected up at an angle with respect to the horizontal with an initial velocity.

– Predict and draw the path that the ball will follow.

PHYSICS MR BALDWIN

Projectiles 25-Oct-13

θ

v

Projectile Motion: A different viewTwo balls start to fall at the same time. The yellow ball has an initial speed in the x-direction. The red ball is just released (dropped).

What do you observe as the balls fall?

It can be seen that vertical positions of the two balls are identical at identical times, while the horizontal position of the yellow ball increases linearly.

Projectile Motion

0cos and sinix i iy iv v v v

In projectile motion, the horizontal motion and the vertical motion are independent of each other, neither motion affects the other.

What is the acceleration of the horizontal motion

zero acceleration

What is the acceleration of the vertical motion

constant downward acceleration of g

The initial velocities are

RECALL FREEFALL MOTION

2

2

1tgtvh i

f iv v g t

g

httgh

2

2

1 2

tgv f

AIM: How can we solve problems involving projectiles? DO NOW: A cannonball is shot out of a cannon at a speed of 20 m/s at an angle of 300 to the horizontal. Calculate the horizontal and vertical components of its velocity?Homework: Your homework sheet will be uploaded onto my webpage. Get it from there. Due FRIDAY.

PHYSICS MR. BALDWINProjectile Motion 30-Oct-13

300

20 m/s

CHECK

cos 20 / cos30 17 /

sin 20 / sin 30 10 /

ix i

iy i

v v m s m s

v v m s m s

Write out your equations of motion for constant and

accelerated motion if you do not have your index card handy.

2 21 1sin

2 2iy iy v t gt v t gt

siny iv v gt

The vertical motion is accelerated motion.

There is a constant downward acceleration g in the vertical direction.

The vertical displacement:

The velocity:

0siniy iv v

How would you describe the vertical motion of a projectile?

ga

Projectile Motion Analyzed

cosix iR x v t v t

There is NO horizontal acceleration. Therefore, the motion is uniform or constant. Horizontal velocity never changes

How would you describe the horizontal motion of a projectile?

cosix iv v The horizontal distance of a projectile is called the RANGE

CHECK• What is the acceleration of a projectile?

– Always constant g &acting downwards

• What is meant by the range of a projectile?

– Maximum horizontal distance

• What is meant by the maximum height of a projectile?

– Height at which the object stops rising

• What happens at the maximum height of a projectile? Is the object still moving?

– Yes. Horizontally.

• What is meant by the time of flight of a projectile?

– The length of time the object is in the air

A cannonball is shot out of a cannon at a speed of 20 m/s at an angle of 300. •What are the horizontal and vertical components of its velocity?•What maximum height did it reach?•How long was it in the air?•How far did it travel?

LET’S ANALYZE THE DO NOW

300

20 m/s

Vertically, what do we know?

smvsma yi /10/80.9 ,2

g

vttgvv

smv

yiyiyf

yf

,,,

,

:Therefore

/0 :path its of At top

ssm

smt 02.1

/80.9

/10for t Solving

2

mtgtvy yi 1.52

1for Solving 2

,max

Horizontally, what do we know?

smvv xxi /17constant isMotion ,

ss

st

t 04.202.12 that. twiceisflight of timeTherefore,

02.1rise tofor time solved We

CHECK. Why do you think that is so?

mssmtvRNow

st

x 7.3404.2/17 :Range the

04.2flight of timefor the solved We

LET’S PLAY HIT THE TARGET.

19

http://phet.colorado.edu/sims/projectile-motion/projectile-motion_en.html

http://jersey.uoregon.edu/vlab/block/Block.html

3-6 Solving Problems Involving Projectile Motion

1. Read the problem carefully, and choose the object(s) you are going to analyze.

2. Draw a diagram.

3. Choose an origin and a coordinate system.

4. Decide on the time interval; this is the same in both directions, and includes only the time the object is moving with constant acceleration g.

5. Examine the x and y motions separately.

Solving Problems Involving Projectile Motion

6. List known and unknown quantities. Remember that vx never changes, and that vy = 0 at the highest point.

7. Plan how you will proceed. Use the appropriate equations; you may have to combine some of them.

Projectile Motion Is ParabolicIn order to demonstrate that projectile motion is parabolic, we need to write y as a function of x. When we do, we find that it has the form:

This is indeed the quadratic equation for a parabola.