projectile motion & vectors test review take good notes!! you may use only these notes on the...

Projectile Motion & Vectors Test Review

TAKE GOOD NOTES!!YOU MAY USE ONLY THESE

NOTES ON THE TEST TOMORROW!!

Projectile motion is the motion of an object in flight including the impact of gravity The path taken in flight is known as a

parabola

Marble/Ramp Vectors

Marble rolls down

the ramp

Marble travels in

the x direction

Marble travels in

the x direction

Vectors A vector is a drawing showing

direction and magnitude

45 mph east

9.8 m/s2

down

A Thrown ball

The quarterback throws the ball at 9 m/s at a 30° angle (to horizontal)

9 m/s

A Thrown ball

The ball moves in the x direction

9 m/s

The ball moves in the y direction

Vectors can add together Vectors can work together to

describe the final, or resultant, vector

For example A boat traveling down a river gets to go

faster because the river “pushes” the boat faster

A boat traveling up river goes slower because it has to go against the river

River Trip

Boat travels 35 mph up river

River travels 10 mph downstream

Result – boat travels 25 mph up river

River Trip

Boat travels 35 mph down river


Result – boat travels 45 mph down river

Vectors can add in any direction!

Boat travels 35 mph across the river


Resultant Boat travels 35 mph across the river


Resultant

You Practice – draw vectors and calculate resultant An airplane flies at 255 mph with a

45 mph tailwind (from behind) A canoeist paddles at 15 mph up

river, while the river flows 3 mph the other way

A swimmer swims at 6 mph across (perpendicular) a river flowing at 2 mph – use a2 + b2 = c2 when vectors are at right angles to each other

You Practice – Answers An airplane flies at 255 mph with a

45 mph tailwind (from behind)

255 mph 45 mph

Resultant = 300 mph

You Practice – Answers A canoeist paddles at 15 mph up

river, while the river flows 3 mph the other way

15 mph 3 mph

Resultant = 12 mph

You Practice – Answers A swimmer swims at 6 mph across

(perpendicular) a river flowing at 2 mph a2 + b2 = c2

62 + 22 = c2 or 40 = c2

6 mph

2 mph

Resultant = 6.32 mph

Calculating the vectors

The y vector = sin of angle X velocity sin(30)*9 m/s Vy = 4.5 m/s

9 m/s

30°

When the football is thrown, it goes upwards at 4.5 m/s

Calculating the vectors

The x vector = cos of angle X velocity cos(30)*9 m/s Vx = 7.79 m/s

9 m/s

30°

When the football is thrown, it goes down field at 7.79 m/s

Vector formulas Vx = cos θ * original velocity

θ is the angle from horizontal Vy = sin θ * original velocity

You Practice – vectors

Find the x and y vectors for the football thrown as shown

12 m/s

50°

Vx = cos(50)*12 m/sVx = 7.71 m/sVy = sin(50)*12 m/sVy = 9.19 m/s

What if it is launched horizontally (no Vy)?

Here is a sample flight with no starting Vy

This is the marble lab we did Monday!!

Distance vs. Time of a Horizontal Launched Object

0

20

40

60

80

100

120

0 1 2 3 4 5

Time (seconds)

Hei

gh

t (m

)

Series1

Horizontal Launching A marble rolls off a table 1.5 m high with a

velocity of 5 m/s How far from the table will it hit the floor? Formulas

d=1/2at2

v=d/t

5 m/s

1.5 m

Use d=1/2at2

to find time it drops (and flies away from the table) 1.5 m = ½(9.8 m/s2)(t2) 3m/(9.8 m/s2)= t2

t2 = .31 seconds2

t =.56 seconds Find the distance

5 m/s=d/.56 seconds 2.8 m = d

5 m/s

1.5 m

You Practice – Horizontal Launching

A marble rolls off a table 3.2 m high with a velocity of 2.5 m/s

How far from the table will it hit the floor? Formulas

d=1/2at2

v=d/t

5 m/s

1.5 m

You Practice - Answers Use d=1/2at2

to find time it drops (and flies away from the table) 3.2 m = ½(9.8 m/s2)(t2) 6.4m/(9.8 m/s2)= t2

t2 = .65 seconds2

t =.81 seconds Find the distance

2.5 m/s=d/.81 seconds 2.0 m = d

5 m/s

1.5 m

Using vectors

A projectile has a curved path as it flies It spends half of its flight time on the

way up, and half on the way down

12 m/s

50°

Using vectors Let’s find how long it takes for

the ball to reach the top of its trajectory, or curved path 12

m/s

50°


How long does it fly? First, we know it goes up at 9.19 m/s Second, we know velocity at the top of the

trajectory is 0 m/s Third, we know that the upwards velocity

decreases at 9.8 m/s2 due to gravity

12 m/s

50°

How long does it fly? Use the formula

a=(Vf-Vo)/t -9.8 m/s2=(0 m/s-9.19 m/s)/t -9.8 m/s2=(-9.19 m/s)/t t=(-9.19 m/s)/(-9.8 m/s2) t=.94 seconds to fly up ttotal = 2*.94 ttotal = 1.88 seconds

12 m/s

50°

How far it fly? First, we now know the time it flies (1.88 seconds) Second, we know the horizontal velocity (vx) = 7.71 m/s Use the formula v=d/t

7.71 m/s = d/1.88 seconds d=7.71 m/s * 1.88 s d = 14.49 m

12 m/s

50°

You Practice – Using vectors

20 m/s

25°


You Practice – How long does it fly?

Use the formula a=(Vf-Vo)/t -9.8 m/s2=(0 m/s-8.45 m/s)/t -9.8 m/s2=(-8.45 m/s)/t t=(-8.45 m/s)/(-9.8 m/s2) t=.86 seconds to fly up ttotal = 2*.86 ttotal = 1.72 seconds

12 m/s

50°

You Practice – How far it fly?

First, we now know the time it flies (1.72 seconds) Second, we know the horizontal velocity (vx) = 18.13 m/s Use the formula v=d/t

18.13 m/s = d/1.72 seconds d=18.13 m/s * 1.72 s d = 31.18 m

12 m/s

50°

projectile motion & vectors test review take good notes!! you may use only these notes on the...

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