Projectile Motion Days 1 & 2

We will learn what projectile motion is and how to analyze it using equations

I will apply my kinematics equations to two dimensions in

projectile problems.

Warm ups 1. Find and pick up your hw quiz and exit ticket from the

lab table.

2. Turn in any missing assignments to the bin.

3. Using what you know about kinematics and how the world works, try to complete the worksheet next to the bin to the best of your ability (we will re-do it together on the back later in the lesson)

4. Take your binder/notebook out for notes.

Projectile Motion This is motion that occurs in two dimensions:

Horizontal motion is at constant velocity Vertical motion is accelerated by gravity

Projectile Motion

The Law of Compound Motion

When an object is moving in multiple directions, the motion in one dimension has no effect on motion in another dimension.

Projectile Motion

Horizontal velocity is maintained by inertia.

Equal distance traveled during each second and constant velocity.

Projectile Motion

Vertical velocity increases each second with the pull of gravity in free fall.

Each second the ball goes 10 m/s faster than the previous second and a greater distance.

5 m 10 m/s 1 s

20 m 20 m/s 2 s

45 m 30 m/s 3 s

80 m 40 m/s 4 s

Projectile Motion

The combined motion looks like this:

The path is not a straight line but an arc of a parabola.

Worksheet from the warm up If 1.0 cm = 5.0 m, the cliff is 80 m high.

It takes about 4 seconds to hit the ground.

Assume g = 10 m/s2 to make easier calculations

How far as it fallen in… 1 second? 2 seconds? 3 seconds? 4 seconds?

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

Projectile Motion

When projectiles are launched at an angle, the initial velocity has a horizontal and a vertical component.

v

vx

vy

Projectile Motion

The path of the cannon ball is in the shape of a parabola. The dimensions of the parabola are determined by the magnitude of the vx and vy components.

vx

vy

Projectile Motion

If the angle of launch is high, velocity vy is much greater than velocity vx. The cannon ball goes higher in the air, but does not go as far.

vx

vy

Projectile Motion

If the angle of launch is low, velocity vx is much greater than velocity vy. The cannon ball goes farther, but does not go as high.

visual

vx

vy

What equations do we use? For the x-direction: 𝑥𝑥 = 𝑥𝑥0 + 𝑣𝑣0𝑥𝑥𝑡𝑡 + 1

2𝑎𝑎𝑥𝑥𝑡𝑡2

v0x= 𝑣𝑣 cos 𝜃𝜃 ax= 0 m/s2

For the y-direction: 𝑦𝑦 = 𝑦𝑦0 + 𝑣𝑣0𝑦𝑦𝑡𝑡 + 1

2𝑎𝑎𝑦𝑦𝑡𝑡2

ay= g = 9.8 m/s2 (directed down) v0y= 𝑣𝑣 sin𝜃𝜃

Always analyze the x-direction and y-direction separately

Example problem The following figure shows an airplane moving horizontally with a constant velocity of 115 m/s at an altitude of 1050 meters. The plane releases a care package that falls to the ground along a curved trajectory. Ignoring air resistance, determine (1) The time required for the package to it the ground (2) How far East the package travels during its fall

(1) Determine the time is takes for the care package to hit the ground

(2) How far to the East has it travelled during its fall?

Example problem A soccer ball is kicked at 17.5 m/s at an angle of 30°

above the horizontal

1. What are the vertical and horizontal components of the

initial velocity? 2. How long (time) is the ball in the air? 3. What is the maximum height it reaches? 4. How far away does the ball land if no one intercepts it?

Example problem A soccer ball is kicked at 17.5 m/s at an angle of 20°

above the horizontal

1. What are the vertical and horizontal components of the

initial velocity? 2. How long is the ball in the air? 3. What is the maximum height it reaches? 4. How far away does the ball land if no one intercepts it?

Projectile Motion

Web simulations.

Links will be on my website.

Archery

Artillery

Homework Projectiles HW # 1 handout

Homework quiz in 2 classes (next week)

Announcement: SNHS will be available for tutoring during SLED starting this week