### KEY

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Unit 4 - Projectile Motion
P're...Test
,cus Questions for the Unit:
• What variables can be manipulated to affect the movement of an object?
~
How do forces govern the motion of objects?
- What are the ways that motion is described, measured, and analyzed in both
horizontal and vertical directions?
1
PART 1: Multiple Choice
1.) A 6 kg block is dropped from the roof of a tall building at the same time a 6 kg ball is thrown
horizontally from the same height. Which statement best describes the motion of the block and - /
the ball?
(1) the block hits the ground first because it has no horizontal velocity
(2) the ball hits the ground first because it has a horizontal velocity
(3) the ball and block hit the ground at the same time because they have the same mass (!) the ball and block hit the ground at the same time because they hav!3 the same vertical acceleration 2.) A baseball player throws a baseball at a speed of 40 mls at an angle of 30 0 to the ground. The
horizontal component of the baseball's velocity is approximately
~\~
(1) 15 mls
(2) 20 mls
(3) 30 mls
~
(1) 35 mls
~
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.
"
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3.) A plane travels 15 kmls due North. A wind of 4 kmls acts due South. What is the resultant
L\\U"n\~ ~ \'5Y-fI\l:,
velocity of the plane?
(1) 19 kmls East
(2) 11 kmls South
0) 11"km/s North
(4) 19 kmls North
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4.) A ball is thrown at an angle of 38 degrees to the horizontal. What happens"to the~of
the ball's vertical velocity during the total time interval that the ball is ip the air?
m
~
(3) It increases then decreases. (4) It remaips the same. Vy.. It decreases then increases.
It decreases, then remains the same;
5.) Which graph best represents the motion of an object in free fall?
iL iL2 IL
~
m
TIME
TIMF
TIME
(1 )
<al
(3)
(4)
6.) A projectile is fired from a gun near the surface of Earth. The initial velocity of the projectile has
a vertical component of 98 mls and a horizontal component of 49 mls. How long will it take the
projectile to reach the highest point in its path?
(1)5s
'
IL
.. ­
010s
(3)20s
V,; Vi~ -'ro.-t
0
'V1- ' ,
v.fqt~\ I I ' \ .
Vi",-;~qrol~ (4)100s
2
(
tn\ ~t
O\~,\:':>-:;;. ~~tnb -r C q·<6:
<u?)
.....J
dw'a'~~
7.) Which two terms both represent vector quantities in physics?
(1) velocity and speed
displacement and acceleration
o
(3) force and distance
(4) speed and displacement
8.) A vector has been broken down into vertical and horizontal components. F1 and F2 • as shown in
FI
the diagram at right.
I
Which of the following vectors best represents the
original vector?
\
\
\
7
(1) -------..
(3)~
(2~
9.) The diagram below shows a student throwing a baseball horizontally at 25 meters per second
from a cliff 45 meters above the level ground. .
• v:25m/s
Approximately how far from the base of the cliff does the ball hit the
ground? [Neglect air resistance.]
(1)45m
(2) 140 m
()75m
(4) 230 m
d.~~~
45('('1::
~ (,\~(5,~-\:?-
t;: 3,02>'&
10.) A child walks 5.0 meters north, then 4.0 meters east, and finally 2.0 meters south. What is the
magnitude of the resultant displacement of the child after the entire walk?
~2fn
(1) 1.0 m
®5.0 m
(2) 3.0 m
(4) 11.0 m
6ro\~t3rtl
'1m
Answer questions 11 and 12 based on the following information:
A stream is 30 m wide and its current flows southward at 1.5 mlsec. A toy boat is launched with a velocity of 2.0 mlsec eastward from the west bank of the stream. 11.) What is the magnitude of the boat's resultant velocity as it crosses the stream?
(1) 0.5 mls
@2.5 mls
(2) 3.0 mls
\
~
\
~\,5'1~
(V".)~I~a. 1- (8Mls')· ""
(4) 3.5 mls
v~
~12.) How much time'is required for the boat·to reach the opposite bank of the stream?
(1)8.6s
® 158
3
(3) 12s
(4)608
~ ..~ ~~
13.) Which graph best represents the relationship between the velocit~ of an object thrown straight
upward from Earth's surface and the time that elapses whil9"it is in the air? [Neglect friction.]
fL ILL
fL I~~
nme
nme
(O
(3)
nnw
'-~~
TIme
0
(2)
14.) If a projectile was launched at 45° instead of 300 , which of the following would you expect to
occur?
(1) it would be in the air a shorter amount of time ~ it would land at a shorter distance @ it would go higher
.
(4) all of the above would occur
15:) The diagram below shows a cannon located 50 m above the ground. When the cannon is fired
a ball leaves the muzzle with a speed of 250 m/s.
Muzzle
\
Which action would most likelyEea"'the time of flight of a ball fired by the cannon?
.
(i) pointing the muzzle toward the ground (2j moving the cannon closer to the edge of the cliff (3) putting the cannon up higher above the ground
(4) firing the ball with a greater initial velocity
16.)An object is dropped from rest and
fallen at the end of one second?
(1) 10 m
05 m
allo~ed to fall freely to Earth. Approximately ho~as it
d~ ~O(d-
(3) 1 m
(4) 20 m
0.-:; ~(\Ot<\ts-)( \&)d.
17.) An object is dropped from rest and allowed to fall freely to Earth. Approximately how@it
falling at the end of one second?
,,~~ V, t (). t;
(J) 10 mls
(2) 5 mls
(3) 1 mls
4
(4) 20 mls
Vr=- 01s \ 0~0(\~
Answer questions 18 and 19 using the graph to the right, which represents the speed vs.
time for a car moving in a straight line.
'-/18.) The car's acceleration is
(1-) 1.0 m1s2
(2) 0.10 m1s2
2
C10mls
(4) 0.0 m1s2
20.
I
'0
19.) The distance the car travels between 1 sec and 2 sec is
(1) 5 m
15 m
(2) 10 m
(4) 20 m
tUI.{\j€...
0
o.xea u'\der
-h
!
10:11111111
o
1.0
2.0
3.0
lime (s)
20.) As shown in the diagram below, a student standing on the roof of a 50.0-meter-high building
kicks a stone at a horizontal speed of 4.00 meters per second.
How muchtffiTiels required for the stone to reach the level grounCrDelow? [Neglect friction.]
.
m3.19s
~5.10s
(3) 10.2 s
(4) 12.5 s
y ::4.00 mls
d~-=- ~Q~a.
~, ~~~\~0t~
t::: 3,\~()
level ground
(Not drawn to scale)
21.) A ball is thrown vertically upward with an initial velocity of 29.4 meters per second. What is the
Vs:'l--==V,7. t ~Qd
maximum height reached by the ball? [Neglect friction.]
(1) 14.7 m
(2) 29.4 m
@)44.1 m
(4) 88.1 m
0'1.:: (a9 N'O\0\ d(-9,~\~~,
22.) Four cannonballs, each with mass M and initial velocity V, are fired from a cannon at different
angles relative to the Earth. Neglecting air friction, which angular direction of the cannon
produces the greatest projectile height?
(4) 20°
(2) 70°
5
23.) The diagram shows a ball thrown toward the east and upward at an angle of 30° to the
horizontal. Point X represents the ball's highest point.
East
---+-­
x
.&
."..,.
~-V---..
.."..,.
~~
~
...... ' -
.
'12
What is the direction of the bali's net force at point X? [Neglect friction.}
~
(!) down
(2) up
(3) west
(4) east
24.} The diagram shows a baseball being hit with a bat. Angle e represents the angle between the
horizontal and the ball's initial direction of motion.
,
"
Which value of would result in the ball traveling the
longest t},orizontal distance? [Neglect air resistance.]
(3) SO°
(4) 90°
PART II: Problem Solving - Answer the following questions in the space provided. SHOW ALL
WbRKI Without all steps, full credit will not be given, even if the answer is correct.
Answer questions 25-27 based on the following diagram and information.
"
Force A with a magnitude of 5.S newtons and force B with a magnitu
concurrently on point P as shown below.
';J.~
25.) Determine the scale used in the diagram.
\C{'<\ ~
B
9.4N
aN
p
2S.} Use a ruler and protractor to construct a vector representing the resultant of forces A and B.
-U? \0
-teA."
27.) Determine the magnitude of the resultan
J.~ Cffi
=
1,6N
6
Aase your answers to questions 28 through 30 on the information and graph below.
A. machine fired several projectiles at the same angle,
e, above the horizontal. Each projectile was
__.ired with a different initial velocity, Vi. The graph below represents the relationship between the
magnitude of the initial vertical velocity. viy. and the magnitude of the corresponding initial velocity,
Vi, of these projectiles.
Inlllal VerUcal Velocity w.
Initial Velocity
'i)'
--E
40.
./
V
i!' 30.
,. V
Co)
0
I­
...
20.
,./" ~
I
./
Jl
1:
~ 10.
JI
•
-
-"H
L
V
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I!
0.0
'Le . . . . r.....
c•••-.
10. . . . . . . .Iw._.~~._'"__
30.
2().
r~"'- 1 - - - ­
40.
50.
eo.
Initial Velocity (mI\$)
~8:}
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Determine the magnitude of the initial vertical velocity of the projectile,
of its initial velocity, Vi, was 40. meters per second.
V'j ,;
29.) Determine the angle,
viy, when the magnitude
.
e, above the horizontal at which the projectiles were fired.
fr1
~
b\ S\(l ~~~)-
-\ (o6
8
e:;o~'1°
30.) Calculate the magnitude of the initial horizontal velocity of the projectile. V;x. when the
magnitude of its initial velocity, Vi, was 40. meters per second. [Show all work, including the
equation and substitution with units.]
V-\".-=- \h cJ)~ o?-+- \,1. ~C2
(J... . ~ (asl'1li)a." (~ctlsY
V'IX ~ ~o{l)I~) ~ .\T~ V; 'I ~ 3\. ~ ('<)/-&
cv:; 3t ~ (\IJ f> 7
.".
,­
Answer questions 31-35 based on the following information.
Tiger Woods hits a golf ball with a total velocity of 45 mls at an angle of 50 degrees above the
horizontal. Assume there is no air resistance.
31.) Sketch the path of the flight for the ball.
-- -
32.) Determine the vertical and horizontal components of the total initial velocity of the ball.
'VIX'" VI CjJiB = ~ 51Y)1")Cc:>s5D" " a~ ,cV'" \s
Vi'J \Ji S\()\j '" (451s) sit) 'CO"; 34. 5 f<1i",
33.) How long is the ball in the air?
Yfj = 'V~ -'r 0.1 _ 3~. 9't1b" 34.5"')\$ -\- (q.~(1)ls» t -t~ 1;04 ~
34.) What is the maximum height reached by the ball?
'If;'"'Vi'j'L 4 ood
O~; (3l-\.':l'1sJ-I- *'\~h)~d
c\~ loO,1m
35.) What will be the horizontal distance traveled by the ball?
0)( :;- \ily.{ d'f;:' C~'!;·9(1l~) (1.tj·h) ~. aOb.5 rY) 8
-
\
".
36.} A plane is flying with a velocity of 30 m/s West while a wind is blowing with a velocity of 10 m/s South. Determine the magnitude and direction of the resultant velocity of the plane. Solve mathematically or graphically. Show all work either way! J
cl t \0"2 ~ c.?­
(\O"\&)" ~ (30"hY ~ C"l
G:: 3cJ<"' Is
.\,,('(\\s
v
~g
(
fesv&\-()() t
'2 \ \ -
(~bu1\cnt-:; u
8~
W()-\
.\l)
('<)\ s (-~S~
e-- icAn-' (Cts)
8~ ,~O SOJ:\-\)
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Answer questions 37-40 based on the information given below.
A long jumper leaves the ground at an angle of 28° above the horizontal. She leaves the ground with an initial vertical velocity of 5.6 mls and an initial horizontal velocity of 10.6 m/s. The jumper lands on the ground 1.14 seconds after she jumps.. 37.} Determine the total (resultant) velocity of the jumper as she leaves the ground.
,~~<.
('Q&\&~~ '2-:-; O:~2--\,'0:::..'"_
2- _ _- ­
resd\-cx*~ J(5,t£,('l)Is)4. ~ (\otot'<'I~)~
V~ \ \.'\ q ('r)\'b
38.) Determine the total horizontal distance traveled by the jumper during the time it is in the air.
d~:; \h'l- t
o'' ll (10.10"'1 5)
-,0
(\.\
'\S') ~ \ d- ,\ f'() 39.) If the speed was kept the same, but the jumper left the ground at an angle of 45°, what will happen to the time the jumper is in the air? (Will time increase, decrease, or remain the same?) (
{\
-e.o:se
, \\v\(
~
5'\~
V\~-;\f\6\(\eo-;Q\.q~t1'\\S)S\()4S--:'~,5mls
_ ~Sr<ll& -;- ~,<o("C)1 s + C
-q .~ls~ t
-t -:; \.135
40.) What will be the maximum height the jumper reaches?
Vr'-~V?- ~ ~",.\
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\~
d3~ V~~ f -;:§; Cb{?-
~
(Q(Y)I~\ (5.b10"~ att)·~h~d
d-=- \,\001
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qr (51o'1~)(O.Sl~ til (..!J~s.:xS1~'
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cb~
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