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```Vectors &
Projectiles
Study Guide
Projectile Review
1. What variable represents
“total horizontal
displacement”?
dx
2. Refer to the diagram • What is the acceleration of the
rock at the beginning right after
it is thrown?
At the bottom right before it
lands?
horizontally = 0m/s2
vertically = 9.8m/s2
3. What is the initial vertical velocity?
0 m/s
4. If the initial horizontal velocity is 45m/s,
what is the horizontal velocity after 2 sec?
45 m/s
What is the horizontal velocity as it hits the
ground?
45m/s (Horizontally velocity remains
constant and never changes)
5. What does range refer to?
The horizontal
displacement of the
projectile
6. For an angled projectile -
Which angle produces the
maximum range?
45-degree
7. If the initial angle is 30 degrees, what other angle will
give the same range? What are these angles called?
What is the relationship between the angle of the
projectile and time in the air?
60o , complementary angles
Larger angle = more time in air
So complementary angles have the same range,
not the same height
8. Define a projectile:
a form of motion in which an object moves
along a curved path under the action of gravity
only.
9. According to the definition
of a projectile why are each
of the following considered
projectiles?
a. a dropped rock
b. a rock thrown horizontally
c. a rock thrown vertically up
d. a rock thrown at an angle
In each case once the rock is
released the only thing acting on
it is gravity
What does the word
“trajectory” refer to?
the path followed by a
projectile
Describe how perpendicular
motions (2-D) (horizontal and
vertical) affect each other.
•They don’t – they are totally
independent of each other.
Which two things below
does the angle of a
launched projectile
affect?
Height
Range
13. If you want to increase the amount of time it takes a
horizontal projectile to land, Which of the following
needs to increase? Height
14. If you want to increase the range of a horizontal
projectile, which of the following needs to increase?
Initial Velocity
15. A 5kg object and a 10kg object are both launched from
the same cliff at the same time. How will the difference in
mass affect each of the following?
a. time to fall
b. range
c. acceleration
d. final velocity
mass has no effect on projectile motion
16. What is the vertical acceleration of:
a horizontal projectile
b. angle projectile
c. dropped object
9.8m/s2
Use the diagram above to answer the following
questions (#17-21):
17. If the Vx = 30m/s at point X what will it be at:
a. point Z?
b. point Y?
c. Point P?
It will be 30m/s at all points (Horizontal
velocity is constant)
18. If the Vy = 15m/s at point X what will it be at:
a. Point Y (0 m/s)
b. Point Z (15m/s)
19. If it takes 2.8s for the projectile to
rise from X to Y how long will it take
for it to fall from Y to Z? 2.8s
20. What is the acceleration of the
projectile at Point Y? at point P?
9.8m/s2 vertically
21. If the projectile above had been
aimed straight up instead of at an
angle at a velocity of 33m/s what
would be the velocity of the object
when it landed?
33m/s
It loses all of its velocity going up
but then gains it all back on its way
down.
Vector Review
What is the difference between a scalar
quantity and a vector quantity?
Scalar: Magnitude only
Vector: Magnitude and direction
What is the symbol for a vector?
• -a vector is represented by an arrow
tipped line segment.
3. How is a resultant drawn on a vector
diagram?
from the tail of the first vector to the
4. What is a tailwind?
wind that blows in the direction of travel
of an object, increases objects velocity
headwind blows against the direction of
travel, decreases objects velocity
For the following
quantities, determine which
are vectors and which are
scalars.
Position (v)
c. Speed (s)
Length (s)
d. Mass (s)
Force (v)
h. Velocity (v)
Price (s)
i. Time (s)
Distance (s)
j. Displacement (v)
6.What is the difference between total
distance and total displacement?
-Distance is a scalar quantity that
refers to "how much ground an object has
covered" during its motion.
-Displacement is a vector quantity
that refers to "how far out of place an
object is"; it is the object's overall change
in position.
7. What is the difference
between a resultant vector
and component vectors?
-The resultant vector
describes the whole vector,
magnitude as well as
direction
-The component vector
describes just one element
of a vector, just like the xcomponent.
Components
Resultant
8. When solving vector
problems, we draw our
diagrams using the head-totail method. What does this
mean?
-the head of this first vector
ends, the tail of the second
vector begins
If you are given 2 component
vectors of varying direction,
what will be the range of the
resultant?
Minimum = subtracting the 2
vectors
vectors.
A stone is thrown horizontally at a speed
of 20m/s from the top of a cliff 80m high.
Horizontal
Vertical
Vx=20m/s
dy=80m
a. How long does it take the stone to reach the bottom
of the cliff?
b. How far from the base of the cliff does the stone
land?
Vector Problems – You must
do the following for each
vector problem on the test:
•
•
•
•
•
Draw a vector diagram to represent the
problem. Label vectors.
Solve the problems mathematically using
the formula(s) provided.
Show the formula(s) used. Show all work.
All answers should be recorded as follows
unless specified differently.
Ex: 12km, 30 degrees, North of West
Put answers in the blanks provided.
Vector Problems –
A runner traveled 15 km west then backtracked 11km east,
then traveled 6km west before stopping. What is the
runner’s total displacement? What is the total distance
walked?
Displacement = 10 km, West
Distance = 32km
15 km west
11 km east
6 km west
While flying due east at 120km/h, an airplane is
also carried northward at 45km/h by the wind
blowing due north. What is the plane’s resultant
velocity? (Magnitude and direction)
_____, _____, ___ of ___
45 km/hr North
Θ
120 km/hr East
Pythagorean
Theorem
c2=452 +1202
c2=16425
c=√16425
c=128 km/hr
Theta
45/120= 0.375
Tan-1 of 0.375
=20.55o
128 km/hr, 21o, North of East
An airplane is flying 340 km/hr at 26 0 North of
east, what would be the north and east
components of the airplane?
θ
•
You would draw the longest vector first (east), then the second
vector
•
•
•
Remember theta is drawn at the tail of the 1st vector
North vector (y-component) = sin(26) x 340 = 149.05 km/hr
East vector (x-component) = cos(26) x 340= 305.59 km/hr
A rocket is launched at an angle of 18 0 S of W with
an acceleration of 118m/s2, what are the rocket’s
vertical and horizontal accelerations?
θ
•
You would draw the longest vector first (west), then the second
vector
•
•
•
Remember theta is drawn at the tail of the 1st vector
South vector (y-component) = sin(18) x 118 = 36.46 m/s2
West vector (x-component) = cos(18) x 118= 112.22 m/s2
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