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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 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
River travels 10 mph downstream
Result – boat travels 45 mph down river
Vectors can add in any direction!
Boat travels 35 mph across the river
River travels 10 mph downstream
Resultant Boat travels 35 mph across the river
River travels 10 mph downstream
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°
Vx = cos(50)*12 m/sVx = 7.71 m/sVy = sin(50)*12 m/sVy = 9.19 m/s
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°
Vx = cos(25)*20 m/sVx = 18.13 m/sVy = sin(25)*20 m/sVy = 8.45 m/s
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°
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