Physics K
Name:______________________________ Period:_____________ Date:____________
Vectors and Projectile Motion Study Guide
Vectors
1. Define the following terms. Make a sketch of a vector and identify each relevant term
on your sketch.
a. Vector
a variable that has both size and direction
b. Scalar
a variable that does not require directional information
c. Magnitude
the size of a vector
d. Orientation
the angle a vector makes with a coordinate system
e. Component
the projections of a vector along the axes of a coordinate system
f. scale factor
the relation between a unit of length and the magnitude in appropriate units it
represents in a vector diagram
g. equivalent vectors
two vectors with the same magnitude and orientation
2. What two different but equivalent ways can you use to specify a vector?
with either magnitude and orientation or using vector components
3. How do you add vectors graphically? Make a sketch to illustrate the steps.
use the tail to tip method, redrawing one vector so its tail starts at the tip of the other
vector and then draw a resultant vector from the tail of the first to the tip of the last
OR find the components of each vector, add the individual components, and then
draw the new vector
4. How is the magnitude of a vector related to its components?. Make a sketch to
illustrate this.
In two dimensions, the components of the vector form the sides of a right triangle so
you can use the Pythagorean Theorem to calculate the hypotenuse which is the
magnitude of f the vector. So x 2  y 2  h 2
5. What is the negative of a vector? Make a sketch to showing a vector and its negative.
The negative of a vector is a vector with equal magnitude but opposite direction
Physics K
Name:______________________________ Period:_____________ Date:____________
Below are some vectors.
A
B
H
C
D
I
E
A
F
A
G
A
6. Which vectors above have the same magnitude?
H, B, C, D, F and A, G
7. Which vectors have the same orientation?
C, I and A, G and E, F
8. Which vectors are equivalent?
A, G
9. Which vector is the negative of vector H?
C
10. Below is a diagram of the forces acting on a ball being swung in a circle on a string. .
1 box = 1 N.
Ftension
Fgrav
a. What are the horizontal and vertical components of the tension force?
x component = 4N
y component = 6 N
b. What are the horizontal and vertical components of the gravitational
force?
x component = 0N
y component = -6 N
Physics K
Name:______________________________ Period:_____________ Date:____________
c. What are the horizontal and vertical components of the net force?
x component = 4N
y component = 0 N
d. What is the magnitude of the tension force? Show your work.
2
(4 N ) 2  (6 N ) 2  Ftension
 7.2 N
11. Put a V in front of the vectors in the following list
e. Position V
l. Net force V
f. Displacement V
m. 20 cm
g. Distance
n. 87 N
h. Velocity V
o. 20 cm right V
i. Speed
p. 9.8 m/s/s down V
j. Acceleration V
q. 87°counterclockwise
k. Force V
r. 90 km/hr West V
12. Below we see a velocity vector diagram in a top view of an airplane being blown off
course by wind coming from various directions.
s. Use vector addition to carefully draw the resultant velocity vectors and
direction of travel for each case.
t. Which plane travels fastest across the ground?
d
u. How do you know?
resultant has longest length
v. Which travels the slowest?
c
w. How do you know?
resultant has shortest length
Physics K
Name:______________________________ Period:_____________ Date:____________
Projectiles
1. Define the following terms:
a. Projectile
an object on which the only force acting is gravity
b. Trajectory
the path of a projectile through space
c. Range
the horizontal distance a projectile travels
2. Draw the free body diagram of a projectile

Fgrav
3. Projectile problems can be divided into two parts:
a. a constant velocity problem in the horizontal direction and
b. a constant acceleration problem in the vertical direction
4. What equations do you use to describe the horizontal motion of a projectile?
v x  v xi
x  vxt
5. What equations do you use to describe the vertical motion of a projectile?
v yf  v yi  gt
g  9.8 m/s/s
y  v yi t  12 gt 2
6. Explain why you could say free fall is a special case of projectile motion.
Free fall is the case where there is no horizontal velocity component to the motion
7. What is the shape of a trajectory of a projectile near the surface of the earth?
parabolic
Physics K
Name:______________________________ Period:_____________ Date:____________
8. Make a sketch of the trajectory of a cannon ball shot from a cannon fired horizontally
from a cliff. Indicate where the cannon ball is at equal time intervals after it leaves the
cannon.using Xs.
9. Describe the spacing between the points in the horizontal direction
The spacings are equal in the horizontal direction
10. Describe the spacing between the points in the vertical direction.
If the object has a positive vertical initial velocity component, the spacings vertically
get smaller and smaller until you reach the peak of the trajectory where the vertical
velocity component is zero. Then the object moves downward and the spacing
Physics K
Name:______________________________ Period:_____________ Date:____________
increasing.
11. At each point in your diagram draw the horizontal and vertical components of the
velocity. In a different color sketch in the resultant velocity vector. above
12. In your diagram label where the cannonball is moving the fastest and the slowest.
Slowest at top and fastest at the bottom most point.
13. Two marbles are launched simultaneously from a physics demo device. One is simply
dropped with no initial velocity, the other is shot horizontally with an initial velocity
of 3 m/s. Which hits the ground first? Explain your reasoning.
The both hit at the same time since the time to hit the ground is determined by the
vertical part of the problem which is identical.
14. A bomb is dropped from a plane traveling at a constant horizontal velocity. When the
bomb is dropped it has no initial velocity with respect to the plane. If the plane
maintains its course where will the bomb land with respect to the plane overhead?
Explain your reasoning
The bomb has the same initial horizontal velocity as the plane when initially dropped.
Since horizontal velocity is constant, if the plane keeps flying straight the bomb will
be directly under the plane at all times.
15. Describe how the mass of the object affects projectile motion
Projectile motion is independent of mass, since the vertical acceleration is always the
same, g=9.8 m/s/s. The mass causes the projectile to be attracted to the planet and
accelerate in that direction.
16. How does the initial angle at which a projectile is shot affect its motion? Make a
sketch to help you explain this concept
The angle changes the vertical and horizontal components of the velocity. The larger
the horizontal component for the same vertical component, the further down range
the projectile will travel. The larger the vertical component for the same horizontal
component, the higher the projectile will reach at its peak
17. On level ground, what initial angle gives the longest range? Why is this so?
45 degrees. Smaller angles have smaller vertical velocity components so the
projectile spends less time in flight. Larger angles and the horizontal component gets
smaller so the projectile goes less far during the time it is in flight. At 45 degrees
these two effects are best balanced.
18. How does the initial velocity of a projectile affect its motion? Make a sketch to help
you explain this concept
The larger the initial velocity at a given orientation, the larger both the vertical and
horizontal components will be, so the flight time and maximum height will increase
because of the larger vertical velocity and the range will increase because you are
moving faster in the horizontal direction
In these short problems you need to show your organized data, the equation you used,
your substitutions, and you must use appropriate units and give directions for vector
quantities.
Physics K
Name:______________________________ Period:_____________ Date:____________
19. A car drives off a 150 m vertical cliff and lands 250 m away from the base of the
cliff. The police ask you, as their physics consultant, to calculate the following.
a. How long was the car in the air before it hit
the ground?
y  150m; g  9.8m/s/s; v yi  0m/s
y  v yi t  12 gt 2
 150m  ( 12 )(9.8m/s/s )t 2
(2)(150m)
 5.5s
(9.8m/s/s)
b. How fast was the car going when it went
over the cliff?
t  5.5s; y  250m
x  (v xi )t
t
250m  vix (5.5s)
250m
 46m/s
5.5s
20. Jocko the clown is shot from a cannon at a 45° angle. so that his initial vertical
velocity is 28 m/s and his initial horizontal velocity is also 28 m/s.
a. How long will it take Jocko to reach the peak of his trajectory?
v yi  28m/s; g  9.8m/s/s; v y  0m/s at peak
v xi 
 28m/s
 2.8s
- 9.8m/s/s
b. What is Jocko’s maximum height at the peak of his trajectory?
v yi  28m/s; t  2.8 s
g  9.8 m/s/s
v y  v yi  gt ; 0m / s  28m/s - (9.8m/s/s)( t ); t 
y  v yi t  12 gt 2  (28m/s * 2.8 s)  ( 12 * 9.8 m/s/s * 2.8 s  )  (78.4m  38.4m)  40m
2
c. How far across the circus ring will Jocko travel before he hits the ground?
v x  28m / s; t  2.8s
x  v x t  28m / s * 2.8s  78.4m