Projectile Motion

Projectile Motion

A projectile can be anything that moves though the air after it has been given an initial “thrust” or input force

Projectiles are only under one force as they move through the air –GRAVITY!

We ignore air resistance in most cases to simply the problems

There are two general categories Projectiles launched horizontally Projectiles launched at an angle

Projectile Motion

Bullet Demonstration Ballistics Cart Demo

Important Concepts

1. Vertical and horizontal motions are independent of each other2. We can relate the height, time in the air, and initial vertical

velocity of the projectile by using its vertical motion, then determine the range (x-distance)

3. We use basic motion equations to solve!

Click on the pictures for animations

What do You Notice??

This is Splat the Cat

Splat the Cat’s days are numbered….Why??

R.I.P

Projectiles Launched Horizontally

Splat the cat is tossed horizontally at 20 m/s off a cliff that is 50 m high.

a) How long is the Splat in the air?

b) How far from the base of the cliff does Splat land?

c) How fast is the cat moving the Instant before he Splats?

Problems Solving Strategy

1. Write known and unknown variables 2. Write variables for x and y directions

yi = 0

yf = -50 mxi = 0 xf = ?

vyi = 0

vyf = ?

vxi = 20 m/s

vxf = 20 m/sWHY?

vnetf = ?

t = ?

ay = g = -9.8m/s2

ax = 0

What’s missing?

Practice Problem #2

A plane that is moving 200 m/s drops a package. The package takes 15 seconds to reach the ground. A) What height was the package dropped from? B) How far did the plane travel from the time the

package was released until the package hit the ground? Is this the same distance the package travels?

C) How fast was the package moving when it hit the ground?

End

Symmetrical Nature of a Projectile

Projectiles at Any Angle..a few differences

When projectiles are launched at any angle, the initial velocity has both horizontal and vertical components

This means that Vo must be used, not just Vxi … we’ve done this before!

Vxi = Vocos

Vyi = Vosin

Horizontal vs. Angled

a of x will ALWAYS be 0 vi of y will ALWAYS be 0

a of y will ALWAYS be -9.8 m/s2

tx = ty

a of x will ALWAYS be 0 a of y will ALWAYS be -

9.8 m/s2

use trig to find vi of x and y

viy = -vfy

The vfy at the peak = 0

tx = ty

Horizontal Projectiles Angled Projectiles

A ball is thrown with an initial velocity of 41.7 m/s at a 70˚ angle

Position

vx vy

1 14.3 m/s 39.2 m/s

2 14.3 m/s 29.4 m/s

3 14.3 m/s 19.6 m/s

4 14.3 m/s 9.8 m/s

5 14.3 m/s 0

6 14.3 m/s -9.8 m/s

7 14.3 m/s -19.6 m/s

8 14.3 m/s -29.4 m/s

9 14.3 m/s -39.2 m/s

1

2

3

45

6

7

8

9

Variables of Motion

Click

Equations

Horizontal Vertical

Other differences and similarities

Time in air is called flight time and ½ of flight time occurs at ½ range

So..it takes the same amount of time to go up as it does to fall down

At ymax, Vyf = 0m/s

Still, only force acting on the is gravity Still, no acceleration in the x direction!

Practice Problem

A football is thrown with an initial velocity of 5.5 m/s at an angle of 49 above the horizontal.

1. How long did it take the ball to return to the launching height?2. What was the maximum height the ball attained?3. What was its range?

range

Max height

Vyf = 0 m/s

Let’s Play Golf

Click

Demos

DistanceFiring anglesHow is time affected? 2nd demo