Unit 3 - Two Dimensional Motion Projectile Motion

What happens to an object when it is airborne?

If it is already in motion and there is no air resistance, it becomes a projectile!

If the object is moving in two dimensions, we can analyze its motion by breaking it into 2, 1D motions.

What happens in the horizontal?

What happens in the vertical?

What happens in the vertical?In the y-direction, there is an acceleration!

Magnitude of a in 2D Magnitude of a in 1D

7.1 8.7372

7.2 7.249

8.8 8.26

9.0 8.9274

9.2 9.315

9.0 ————

It is the same as if it was dropped!

What factors influence the trajectory of a projectile?

What happens in the horizontal?

In the x-direction, there is no acceleration!

In the simulation, the x-component of the velocity vector remains the

same length!

vox = vfx

ax = 0 m/s2

What happens in the vertical?

In the simulation, the y-component of the velocity vector gets longer

over time.

vfy = voy + ayt

ay = 9.8 m/s2

Because there is a constant acceleration, the kinematic equations can be applied!

How does launch height affect the range of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does launch height affect the airtime of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does launch velocity affect the range of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does launch velocity affect the airtime of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does mass affect the range of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does mass affect the airtime of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does air resistance affect the range of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

How does air resistance affect the airtime of a projectile?

1. It causes it to increase.

2. It causes it to decrease.

3. It has no effect.

Depends on the amount of air resistance!

How does launch angle affect the motion of a projectile?

The higher the angle, the greater the maximum height.

There is an a parabolic relationship between angle and range.

Predicting The Trajectory of A Projectile

As an object in free fall, a projectile’s motion can be described by the same equations that we used for one dimensional motion.

Because there is no acceleration in the x-direction, we can simplify those equations!

x-direction

x = 1/2axt2 + voxt + xo

vfx = vox + axt

vfx2 = vox2 + 2ax(x-xo)

y = 1/2ayt2 + voyt + yo

vfy = voy + ayt

vfy2 = voy2 + 2ay(y-yo)

y-direction

X x = voxt + xo

X vfx = vox

X

Staying Organized!

Because there is motion in two dimensions, we have twice the information to keep track of!

Use the question to complete as much of the table as possible!

What do you always know?

0 m/s2 -9.8 m/s2

vovf

Disp.

t

a

Double Table

x y

Let’s Give it A Try!

A soccer ball is kicked at an angle of 60° with an initial velocity of 40.0 m/s.

The components of the initial velocity!

vovf

Disp.

t

a

Double Table

x y

What can you figure out from this information?

0 m/s2 -9.8 m/s2

vo

vox

voyθ

vox = vocosθ

voy = vosinθ

20 m/s 35 m/s

20 m/s

How High Can the Soccer Ball Go?

x-velocity is still the same!

vovf

Disp.

t

a

Double Table

x y

What do you know about the soccer ball at the top of its path?

0 m/s2 -9.8 m/s2

20 m/s 35 m/s

20 m/s

y-velocity is 0 m/s!

0 m/s

?

Do we have enough information to solve?

vfy2 = voy2 + 2ay(y-yo) ymax = 62.6 m

What is the soccer ball’s range?

The y-displacement is 0 m!

vovf

Disp.

t

a

Double Table

x y

To determine the range, we must determine the airtime.

0 m/s2 -9.8 m/s2

20 m/s 35 m/s

20 m/s

o m

Do we have enough information to solve?

?What do we know?

Airtime is determined by gravity!

?

x = voxt + xo vfx = vox

What is the soccer ball’s airtime?

vovf

Disp.

t

a

Double Table

x y

Do these times make sense?

0 m/s2 -9.8 m/s2

20 m/s 35 m/s

20 m/s

o m?

The airtime is 7.1 seconds!

?

y = 1/2ayt2 + voyt + yo

0 = 1/2ayt2 + voyt

0 = t(1/2ayt + voy)

t = 0 sec and t = 7.1 sec

7.1sec

What is the soccer ball’s range?

vovf

Disp.

t

a

Double Table

x y

Could you solve for the y-velocity just before it hits the ground?

0 m/s2 -9.8 m/s2

20 m/s 35 m/s

20 m/s

o m?

x = 142 m

7.1sec x = voxt + xo

vfy = voy + ayt vfy = - 35 m/s

142 m

Let’s Try Another One!

Bullseye

What’s the role of inertia?

How does this relate to two-dimension motion?

Because there is no force in the x-direction, the object keeps moving horizontally!

Dealing with Air Resistance

How are we doing?

Let’s Figure it All Out!

vovf

Disp.

t

a

Double Table

x y

A javelin thrower releases the javelin at an angle of 30°. If the initial velocity is 25.00 m/s, what is:

The maximum height of the javelin?

The airtime of the javelin?

The range of the javelin?

The final velocity in the x-direction?

Solve it on your whiteboard!

How Did You Do?

vovf

Disp.

t

a

Double Table

x y

A javelin thrower releases the javelin at an angle of 30°. If the initial velocity is 25.00 m/s, what is:

The maximum height of the javelin?

The airtime of the javelin?

The range of the javelin?

The final velocity in the x-direction?

Solve it on your whiteboard! 0 m/s2 -9.8 m/s2

21.7 m/s 12.5 m/s

7.97 m

2.55 s

55.23 m

21.7 m/s