PowerPoint Presentation

Projectile Motion1Projectile MotionThe path that a moving object follows is called its trajectory.

Projectile motion involves the trajectories and velocities of any object that has been launched, shot, or thrown.2Does this represent a realistic trajectory?Yes. No. Maybe.

3(Speed: when the bus jumps; Spider-man 2: when he suddenly loses his web power.)

Does this represent a realistic trajectory?

4(Speed: when the bus jumps; Spider-man 2: when he suddenly loses his web power.)

Does this represent a realistic trajectory?Yes. No. Maybe.

The coyote would not go straight horizontally, pause, and then fall straight down. You see unrealistic trajectories all the time in media. Can you think of any others? 5(Speed: when the bus jumps; Spider-man 2: when he suddenly loses his web power.)

RulesThere are only a few rules we have to follow:

All projectiles are freefalling vertically with an acceleration of 9.8 m/s2 downwardsHorizontal motion is totally unaffected by gravity!Since there are no forces acting on it, a falling objects horizontal velocity is constant!6

Visualizing Projectilesfirst enter vectorsfocus on vxvx is constant the whole flight!7

Visualizing Projectilesfirst enter vectorsfocus on vxfocus on vyvy decreases as it rises!by how much per second?no vy at the top!8

Visualizing Projectiles9X equationsY equations

0Horizontal ProjectilesHorizontal motion is constant there is no acceleration Only formula used in horizontal (x) direction is:

vx = dx / tconstant speed!11note the distance traveled in each is the same in the x directionHorizontal ProjectilesHorizontal projectiles are not thrown up or down. They are moving horizontally and falling verticallyThe only initial velocity is in the x directionVertical velocity (vy) is gained by freefall

viy = 0

since viy is in freefall,

a = -9.8 m/s2

12HORIZONTAL PROJECTILE pg 288A rock is thrown horizontally from the top of a cliff at a constant speed of 15 m/s. Calculate the horizontal & vertical positions of the rock after each second and place these positions in the table below. Assume the rock is freefalling from rest.

ANGLED PROJECTILE pg 289A rock is thrown at an angle of 30 from the top of a cliff. Calculate the horizontal & vertical positions of the rock after each second and place these positions in the table below.

X equationsY equations

Measure his height, Find the scale of the picture. Lets analyze the jump

dmax16Lets analyze the jump

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http://www.physicsclassroom.com/mmedia/vectors/pap.cfmVariable Definitions:

vyi initial velocity in y directionvx = constant velocity in x directionv final velocity of projectiledx horizontal range dy Heightdy Maximum altitude dy Vertical displacement

Hitting a TargetIf the rifle is fired directly at the target in a horizontal direction, will the bullet hit the center of the target?

Does the bullet fall during its flight?

20start by drawing a picture:ExampleA person decides to fire a rifle horizontally at a bulls-eye. The speed of the bullet as it leaves the barrel of the gun is 890 m/s. Hes new to the ideas of projectile motion so doesnt aim high and the bullet strikes the target 1.7 cm below the center of the bulls-eye.

What is the horizontal distance between the rifle and the bull s-eye?label the explicit givens with subscript. Ex: dx or dy

21givens (separate by direction):Example

What is the horizontal distance between the rifle and the bull s-eye?unknown:

XY

horizontal displacement

22which equation do we use?Example

use to find timerewrite equation for t

23Use t and vx to solve for dxExample

24Non-horizontal Projectiles vx is still constant vy is still in freefallonly difference with non-horizontal isnow the object begins with a vertical velocity!

25Non-horizontal ProjectilesAngled Projectiles require a little work to get useful vivi has an x and y componentneed to calculate initial vx and vy

26Breaking up a vectorevery vector has 2 components to ita horizontal componenta vertical component

they add up to the total

27Breaking up a vector SOHCAHTOA

hypotenuseadjacentopposite

28Breaking up a vector SOHCAHTOAneed to find ?

hypotenuseadjacentopposite

29Non-horizontal Projectilesneed to calculate initial vx and vy

30

1. Start by drawing a picture:Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. How long is the stone in flight? vi = 31.5 m/s

vxvyi2. Find the initial velocity in the x and y directions

31XY

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. How long is the stone in flight?

vxvyi

Decide upon initial and final conditionsvi = 31.5 m/s32Find the velocity when the ball hits the ground, then find the time it takes to get there.

Use the quadratic formula

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. How long is the stone in flight?

vxvyiThere are 2 ways to solve

vi = 31.5 m/s33

EquationsAngled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. How long is the stone in flight?

vxvyi

abcSolve using Quadratic formula or GRAPH it!vi = 31.5 m/s34

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. How long is the stone in flight? vo = 31.5m/s

vxvyo

When is the stone on the ground?t = 7.00s35XY

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. What is the range of the stone?

vxvyo

Equations

vi = 31.5 m/s36XY

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. What speed does the stone hit the ground?

vf = ?vxvyf37

Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. What speed does the stone hit the ground? vx

vf = ?vyf38

Givens Angled Projectile ExampleA stone is thrown off the top of a building from a height of 45.0 m. The stone has a launch angle of 62.5 and a speed of 31.5 m/s. What speed does the stone hit the ground? Equationsvx

vyfvf = ?39Varied Angles

which projectile angle shoots highest?larger means faster viywhich projectile angle shoots farthest?45 has perfect balance of fast vx and long flight time.

40Practice pg 298

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426. When he leaves the ramp he is 1.5 m above the ground, moving at 14 m/s and 18 above the horizontal. If each of his friends is 0.60 m wide, what is the maximum number of friends over which the cyclist can jump

1.5 m above thegroundhorizontal. If each of his friends is 0.60 m wide what is the maximum number of friends over which the cyclist can jump?v = 14 m/sXY

14 m/s and 18 above the horizontal.

When he leaves the ramp he is 1.5 m above the ground, moving at 14 m/s and 18 above the horizontal. If each of his friends is 0.60 m wide, what is the maximum number of friends over which the cyclist can jump?XY

1. Find twhich equation do we use?We could use to find time

But you would have to use the quadratic formula to solve for t because there is a t and t2When he leaves the ramp he is 1.5 m above the ground, moving at 14 m/s and 18 above the horizontal. If each of his friends is 0.60 m wide, what is the maximum number of friends over which the cyclist can jump?XY

1. Find twhich equation do we use?Instead, find vyfAnd then find t:

vyf = - 6.9 m/st = 1.14 sWhen he leaves the ramp he is 1.5 m above the ground, moving at 14 m/s and 18 above the horizontal. If each of his friends is 0.60 m wide, what is the maximum number of friends over which the cyclist can jump?XY

2. Find dxvyf = - 6.9 m/st = 1.14 s

3. How many friends?

Varied Angles

which projectile angle shoots highest?larger means faster viywhich projectile angle shoots farthest?45 has perfect balance of fast vx and long flight time.

47`

For the following situations: State if the following are positive, negative or zero.

vovax3. Calculate the maximum altitude of the ball (from the floor).

XY

?0 m/svfy

vfyvy =

3. Calculate the maximum altitude of the ball (from the floor).

XY

?0 m/s

vfy= from #2vy =

1. Find twhich equation do we use?

Percent Error Formula, last pg of text

*Known = your calculation