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Unformatted text preview: MasteringPhysics 8/20/09 11:00 AM Print Version with Answers ‘ HW1  under construction!
Due: 11:59pm on Wednesday, September 2, 2009 Note: You will receive no credit for late submissions. To learn more. read your instructor's diing Pong Converting Units: The Magic of l geommww, . . . .. s...,..,....t._.,,_,.,,,...,,M, ,. W ,,,,,,., HM. ow “MW, ., s, ; Description: Explains method to convert units. then has several examples. the hardest being velocity mmnmmmmmtw ; Learning Goal: To learn how to change units of physical quantities. Z Quantities with physical dimensions like length or time must be measured with respect to a unit, a standard for quantiﬁes with
this dimension. For example, length can be measured in units of meters or feet, time in seconds or years, and velocity in meters
3 per second. 3 When solving problems in physics, it is necessary to use a consistent system of units such as the International System (abbreviated SI. for the French Systéme International) or the more cumbersome English system in the SI system, which is the
preferred system in physics, mass is measured in kilograms. time in seconds, and length in meters. The necessity of using ‘
consistent units in a problem often forces you to convert some units from the given system into the system that you want to use
.3 for the problem. ; The key to unit conversion is to multiply (or divide) by a ratio of different units that equals one. This works because multiplying
' any quantity by one doesn't change it To illustrate with length, if you know that 1 indx : 2.54 rm. you can write 1 M 2.54 cm
—. 1 inch ‘ V To convert inches to centimeters, you can multiply the number of inches times this fraction (since it equals one), cancel the inch
unit in the denominator with the inch unit in the given length, and come up with a value for the length in centimeters To convert
, centimeters to inches, you can divide by this ratio and cancel the centimeters. ; For all parts, notice that the units are already written after the answer box; don't try to write them in your answer also. I i 832,35; 01371;». a t ‘ Express your amer in centimeters to three signiﬁcant ﬁgures \
“in ; ANSWER: '25“; Cm _ lax/4,» cal/Dom. : Sometimes you will need to change units twice to get the ﬁnal unit that you want. Suppose that you know how to convert from E
i ntimeters to inches and from inches to feet. By doing both in order you can convert from centimeters to feet. E
éSuppose that a particular artillery piece has a range R = 1.997x104 yank. Find its range in miles. Use the facts that
ilmjlazs280ftand 3ft:1ymd. Convert yards to feet The first step in this problem is to convert from yards to feet, because you know how to then convert feet into miles. Convert i
L997><io4 yank into feet. Use 3ftv Express your answer in miles to three signiﬁcant ﬁgures. 1.997xio4 “his = W52g) mum meats/MM i
g ANSWER: 3,3
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u lmile 1‘ ANSWER: ' v=1609 m/hom’ ll 2e , ANSWER: Hg, .. . i‘llwur
’lhour
ivth Express your answer in meters per second to three signiﬁcant ﬁgures. I
: ANSWER! . : p = 0447 m/s l
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r Notice that by equating the two values for (7. you get 1 mph 2 0,447 111/3. It might be valuable to remember this, as you may frequently need to convert from miles per hour into more useful SI units. By remembering this relationship in
the future, you can reduce this task to a sinole conversion. Description: All of the quantities that follow will occur frequently in your study of physics. (a) Express the speed of light 3.00
* 10M 8) (m/s) in mi/sl (b) Express the speed oflight in mph. (0) Find the speed of sound in air at O degree(s) C( 1100 ft/s... All of the quantities that follow will occur frequently in your study of physics.  as u WWW _ _. , ..................................................................... .7 r.
Part A l Express the speed oflight Gun X 103 m/s) in mile. ANSWER: L http://session.masteringphysics.com/myct l MasteringPhysics Steam) Find the speed of sound in air at 0 CC( 1100 ﬁlls ) in mph. /, * v = i i
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P? Problem 1.18: Blood is thicker than water. Description: The density (mass divided by volume) of pure water is 1.00 glcmAB that of whole blood is 1.05 g/cm"3 and the
density of seawater is 1.03 g/cmA3. (a) What is the mass of ## L of pure water? (b) What is the mass of ## L of whole blood?
(0) What is The density (mass divided by volume) of pure water
is 1.00 am? that of whole blood is 105 g/cnﬁ’ and the density of seawater is 1.03 g #1133. gPanA :ANSWER: ., H What is the mass of 3.00 L of pure water? i
i What is the mass of 3.00 L of seawater? , ANSWER: , l
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L Description: This problem asks students to ﬁnd the components of graphed vectors; no trigonometry is involved. Shown is a 10 by l0 grid. with coordinate axes x and y The grid runs from 5 to 5 on both axes. Drawn on this grid are
four vectors, labeled 3' duough This problem will ask you various questions about these vectors. All answers should be in
decimal notation. unless Otherwise speciﬁed. Part A E What is the x component of X? r.._._____ ____________ ,#_~_.w* ...... ._ ...... v. ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, s _»V____Mm_mws How to derive the component A component of a vector is its length (but with appropriate sign) along a particular coordinate axis, the axes being specﬁed in
3 advance. You are asked for the component of jf that lies along thex axis, which is horizontal in this problem. Imagine two i L 1' Hint A.l
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v a}: m=1.03v g A WI Components of Vectors 2 8/20/09 11:00 AM Page 3 of 14 MasteringPhysics lines perpendicular to the .r axis running from the head (end with the arrow) and tail of down to the x axis. The length of ) the x axis between the points where these lines intersect is the x component of X . in this problem. the 2: component is the x coordinate at which the perpendicular from the head of the vector hits the origin (because the tail of the vector is at the l E Hint CJ Consider the Motion Don't forget the sign. L... ‘ Wﬁwwmmu mews... 7.... . .. . WW Express your answer to the nearest integer. /, i ANSWER::...., . . .
t By = ‘ What is the x component of (77
i Hint DJ How to ﬁnd the start and end points of the vector components i A vector is deﬁned only by its magnitude and direction. The starting point of the vector is of no consequence to its deﬁnition
Therefore, you need to somehow eliminate the Starting point from your answer. You can run two perpendiculars to the x axis, one from the head (end with the arrow) of and another to the tail, with the .r component being the difference ‘ between x coordinates of head and tail (negative if the tail is to the right of the head). Another way is to imagine bringing the i tail of to the origin. and then using the same procedure you used before to ﬁnd the components of and I; This is
l ‘ equivalent to the previous method. but it might be easier to visualize. L s _ __ .H._s_s_.~_m._.,.News‘sm... ,A‘_.s WW we", s." sh.._ v.s.ss .. v...” MW. . _.... m 1 Express your answer to the nearest integer. i ANSWPlkz _ “2 / Q , r.
i g The followmg questions W1“ ask you to give both components of vectors using the ordered pairs method. in this method, the): l g component is written ﬁrst, followed by a comma and then the y component. For example, the components of would be written 2.5.3 in ordered pair notation. Essences LThe answers below are all integers, so estimate the components to the nearest whole number. Part E i in ordered pair notation, write down the components of vector i
3 Express your answers to the nearest integer. i ANSWEm, ._ 2 .
i I 33,3” = 3 / l i in ordered pair notation, write down the components of vector ; Express your answers to the unrest integer. I ANSWER: . . .. http2//session.masteringphysics.com/myct 8/20/09 11:00 AM Page 4 of 14 MasteringPhysics r 8/20/09 11:00 AM What is true about 5 and 137 Choose from the pulldown list below. i: . r  ANSWER ,, Often a vector is speciﬁed by a magnitude and a direction; for
example, a rope with tension f exerts a force of magnitude T in a direction 35° north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a
coordinate system and manipulate the components of the vectors in
that coordinate system. Part A
l Find the components of the vector x with length a = LOO and angle 0:200" with respect to the x axis as shown. l
i WWW ...... “wwhﬁw MMMMMMMMM hm»... ....... .MM _. _._._.. M ._._. _,_ __.__._~.___,..m . Hint AJ What is the :5 component? = book at the ﬁgure shown. i I, points in the positive x direction. so A, is positive. Also. i the magnitude EAT! isjust the length 0L 2 03400301) ; ANSWER: H i ’5 = We) Enter the x component followed by the y component, separated by a comma. grants Find the components of the vector 1} with length b = mo and angle 5:201)" with respect to thex axis as shown. r...“ M x
IHint B.) Whuktlcxmpount? i
i The x component is still ofthe same form. that is, Lmsw). L...4._...‘..V__l;;l_;_..;;_m~.__i Enterthexcompmtfﬂﬂedbylbymﬁc’u’ddbyam B = Nah?) The components of 1; still have the same form. that is. (st(0). L sin(8)). despite E‘s placement with respect to the http:/[session.masteringphysics.com/myct Page 5 of 14 MasteringPhysics 8/20/09 11:00 AM Method leind theugletlnt émkeswahthepodovexuss The .r component is still of the same form, that is. L 303(0). where 0 is the angle that the vector makes with the positive x axis . Hint 02 Method 2: Use vector addition v book at the ﬁgure shown 1 1 (7 z 5', + C} 2' iézi = EWNQR) == Céiﬂwi 3. C,, the xcomponent of C" is negative. since 0‘, points
in the negative x ' Use this infotmation to ﬁnd Cx . Similarly, ﬁnd 0". Enter the x component followed by the y component, separated by a comma. j ANSWERzy mnw CK r}: z. E
e 5 ii f\ “< Problem 1.36 Ti Description: A ladybug starts at the center ofa ## in.~diametcr turntable and crawls in a straight radial line to the edge. While
this is happening. the turntable turns through a ## degree(s) angle. (a) Find the magnitude of the ladybug's displacement vector. A ladybug starts at the center of a 16.0 in :diameter turntable and crawls in a Straight radial line to the edge. While this is memmmmwmimm happening, the turntable turns through a 600° angle. X Part A 0”“ " \ ‘
i ﬁnd the magnitude of the ladybug's displacement vector. i
l ANSWER?“ _, ,, / 1: M u. Part B V V . _
Find the direction of the iadybug‘s displacement vector. ‘ t m ‘ it. Please express your answer as an angle between the displacement vector and the initial direction of the i Problem 142 x r: _ ___._ _ .......... WM ________ "my '— pa,
Description: A woman takes her dog Rover for a walk on a leash. To get the little pooch moving forward, she pulls on the Z leash with a force of F at an angle of #If degree(s) above the horizontal. (a) How much force is tending to pull Rover forward?
V (b) How... A woman takes her dog Rover for a walk on a leash. To get the little pooch moving forward, she pulls on the leash with a force 9 http://session.masteringphysics.com/myct Page 6 of 14 MasteringPhysics 8/20/09 11:00 AM of 23.0 at an angle of 320” above the horizontal. Part A
l i How much force is tending to pull Rover forward? gnNswanzj PM: Postal N V‘ I . A v  3': 7&2 y
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53“; _, , . z How much force is tending to lift Rover off the ground? i
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L....,. _ ______________ .M. M ,,,,,,, MM I V Prlem 1.46 Description: A plane leaves Seattle, ﬂies ## mi at ## degree(s) north of east. and then changes direction to theta2 south of
east. After ﬂying at #4! mi in this new direction, the pilot must make an emergency landing on a ﬁeld. The Seattle airport facility... U A plane leaves Seattle. ﬂies 791) mi at 180" north of east. and then changes direction to 490° south of east. After flying at =
119 mi in this new direction. the pilot must make an emergency landing on a ﬁeld. The Seattle airport facility dispatches a rescue crew. ’ I qﬁ M , \ iranA ‘ ' . v. .. )W“
I In what direction should the crew fly to go directly to the field? Use components to solve this problem. ‘ O
ANSWER: an: r: 41 or ‘
m" ‘13" m 62% ’0 S E“ g //
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5.2:}. x l S Q : ANSWER" d = J(d25in(92)~d1sin(01))"+(d2ms(92)+dlom(01))2 i
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E How far should the crew fly to go directly to the ﬁeld? Use components to solve this problem.
i gr What it vs. t Graphs Can Tell You WT
l Description: Find average and instantaneous velocity given an x vs. t graph. The relation between area under the v vs. tcurve Dﬁm I (at V
and distance traveled is presented.
To describe the motion of a particle along a straight line, it is often convenient to draw a graph representing the position of the q wQ ‘3 I 0
particle at different times. This type of graph is usually referred to as an .r vs. I graph. To draw such a graph, choose an axis ““ 0
system in which time t is plotted on the horizontal axis and position 1; on the vertical axis. Then. indicate the values of x at i various times (. Mathematically. this corresponds to plotting the variable 3: as a function of t. An example ofa graph of position L S m 'g as a function of n'me for a particle traveling along a straight line is shown below. Note that an x vs. t graph like this does not
represent the path of the particle in space. ............ .Wmmwmm..mwwmmw,ws“mums,”n..._w..mw.m.__.WW...MM.MMM_MM_M..
ow etsstu y egrap s own in e igurern more etai. E1} l ' d til it h ' Ill f ' d 'l i Refer to this graph to answer Parts A, B, and C. x (m) X=3©Wt WWWHS) 40 50 iPartA W
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I What is the total distance A; traveled by the particle? 2 _ jst e._.‘s’*9,§ _________ ,. : ,....__m., MWWAA ,. A W _. ._ ..,,_..._._,_._M _ .._.H _N__._. .s A‘s . a.. l Hint A.l Total We 1 E The total distance A; traveled by the particle is given by the difference between the initial position 1:0 at t 7.: 0,0 ,5 and the l l http://session.masteringphysics.com/myct Page 7 of 14 MasteringPhysics in the plot shown in the ﬁgure. 1 316.0 m at be 10.0 at /,, l Hint 3.] Deﬁnition and graphical interpretation of average velocity
The average velocity v... of a particle that travels a distance A: along a straight line in a time interval A; is deﬁned as , . § , In an x vs. I graph, then, the average velocity equals the slope of the line connecting the initial and ﬁnal positions. Hint 8.2 Slope of a line The slope ,7; oh line from point A. with coordinates (IA, 3“), to point B.with coordinates (IB,yB). is equal to the "rise" ; over the "run," or 1
Express your answer in meters per second. ANSWER: ., . .. The average velocity of a particle between two positions is equal to the slope of the line connecting the two
corresponding points in an x vs. t graph. nstantaneous velocity at any point is equal to the slope of the line tangent to the curve at that point. t..___e~ ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, tw__&~ 7*; ...................................... ea_ eeeeee ._ ......... .__..f___.e ._.__.__ ..... a. Express your answer in meters per second. The instantaneous velocity of a particle at any point on its x vs. t graph is the slope of the line tangent to the curve at that
point Since in the case at hand the curve is a straight line, the tangent line is the curve itself. Physically, this means that i
the instantaneous velocity of tlte particle is constant over the entire time interval of motion. This is true for any motion where distance increases linearly with time. i
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E {Another common graphical representation of motion along a straight line is the v vs. 1 graph, that is. the graph of
(instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the ‘ vertical axis. Note that by deﬁnition, velocity and acceleration are vector quantities. ln straightline motion. however, these
i vectors have only one nonzero component in the direction of motion. Thus, in this problem. we will call v the velocity and a u Lthqe acceleration, even though they are really the components of the velocity and acceleration vectors in the diremion of motion. E
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i E graph of the panicle's motion. you can determine the instantaneous velocity of the particle at any point in the curve. The
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i B r,( mm 03% 0.0 E 0.4 \u\
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0.6 r
(H : 0.2; ANSWER: fW”GraPh A 76mph B
L'Graph C
ivfGraph D Compare this result with what you found in Part A. As you can see, the area of the region under the v vs. t curve equals
the total distance traveled by the particle. This is true for any velocity curve and any time interval: The area of the region
that extends over a time interval A: under the V vs tcurve is always equal to the distance traveled in At. in m 20 30 40 50' E
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g oi 1020 30 4o 56"”
i i C : “(m/s) 5 02 m 20 30 40 50”” D 1‘11,"th
0.8% or) kWmw 0.4: g
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()..E "(SimiiiwiiTso 40 56’ ’ ‘5’ Whenever a particle moves with constant nonzero velocity, its x vs. t graph is a straight line with a nonzero slope, and its
v vs, tcurve is a horizontal line. Shown in the ﬁgure is the V vs tcurve selected in the previous part. What is the area A of the shaded region under the curve? Uri m/s) 0.8
0.6 0.4 3040 i
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i Description: Given a plot of position vs. time, determine average velocity over different time intervals. Learning Goal: To learn to read a graph of position versus time and to calculate average velocity. in this problem yon will determine the average velocity of a moving
object from the graph of its position ﬁnes a function of time t. A traveling object might move at different speeds and in different
directions during an interval of time, but if we ask at what constant
2 velocity the object would have to travel to achieve the same httpzl/session.masteringphysics.com/myct Average Velocity from a Position vs. Time Graph ieters) 8/20/09 11:00 AM Page 9 of 14 MasteringPhysics 8/20/09 11:00 AM i displacement over the given time interval, that is what we call the
object’s average velocity, We will use the notation “with t4] ‘0 indicate average velocity over the time interval from t, to t1. For
instance. 7541.3} is the average velocity over the time interval Position (n
g : fromtmltorxa 0 l 2 3 4 h 6 Ti me i seconds) i Hint AJ Deﬁnition of average velocity
[_
l i Average velocity is deﬁned as the constant velocity at which an object would have to travel to achieve a given displacement l (difference between ﬁnal and initial positions. which can be negative) over a given time interval, from the initial time (i to !
,form, average velocity is given by ii the ﬁnal time LP The average velocity is therefore equal to the displacement divided by the given time interval. In symbolic
l K Answer to the new huge. l
l ANSWER:
E emit). 1} = 0 Find the average velocity over the time interval from i to 3 seconds mm 3.1 with a. m“”‘”’“‘”;:.‘.;sio.. ' The ﬁnal and initial positions can be read off the y axis of the graph. What is the displacement during the time interval from
I to 3 seconds? Express your answer numerically, in meters 1! I: ANSWER:
1 It “xi = 40 in ‘ l Average velocity is deﬁned as the constant velocity at which an object would have to travel to achieve a given displacement " '
(difference between ﬁnal and initial positions. which can be negative) over a given time interval, from the initial time 1‘ to l the ﬁnal time if. The average velocity is therefore equal to the displacement divided by the given time interval. In symbolic
form. average velocity is given by ; Express your answer in meters per second to the nearest intact. {é ANSWER: ' 7 i y y i ml ' vmll, 3} = 20 m/s 1 we” ~
.__E__.___.____W.,,...._VW.WWM..“MWAWWEWW. w _______ ﬂ. __________ _. W... l
A note about instantaneous velocity. The instantaneous velocity at a certain moment in time is represented by the slope of l
the graph at that moment. For straightline graphs, the (instantaneous) velocity remains constant over the interval, so the instantaneous velocity at any time during an interval is the same as the average velocity over that interval. For instance, in
this case. the instantaneous velocity at any time from 1 to 3 seconds is the same as the average velocity of 20 m/s. g3 Since the object‘s position remains constant from time 0 to time Lthe object's displacement from 0 to 3 is the same as in
l Part B. However. the time interval has changed. 1
i Give your answer to the: signiﬁcant ﬁgures.
3 ( ANSWER: : , ., _. vm[ﬂ.3]= 13‘3 m/s e... Note that [Emio‘ 3} is not equal to the simple arithmetic average of emit)~ 1] and limit, 3]. Les because they are averages for time intervals of different lengths. http://session.masteringphysics.com/myct Page 10 of 14 MasteringPhysics 8/20/09 11:00 AM Hint 0.] Determine the displacement What is the displacement? 40
m Hint D.2 Determine the time interval What is the time interval? Answer to two signiﬁcant ﬁgures. ANSWER: H i it ~ ti = as i Express your answer to three Wat “guns : ANSWER: _ 133 Finally, ﬁnd the average velocity over the whole time interval shown in the graph. Hint E.l Determine the displacement
What is the displacement? Answer to the nearest integer. dam—nook 0 m \, , , WNW, m, ,, WM. ,w WNW HM. Express your answer to three Wt ﬁgures. ; ANSWER: n
; vm[0.0, 6.0% = m/s “""’”' W /' “WA object was standing still the entire time! Problem 2.10: Hypersonic scramjet. 3 Description: On March 27, 2004, the United States successfully tested the hypersonic X'43A scramjet, which ﬂew at Mach 7
(seven times the speed of sound) for ## seconds. (A scramjet gets its oxygen directly from the air, rather than from fuel.) (a) At
this." ‘ On March 27, 2004. the United States Successfully tested the hypersonic X‘43A scramjet, which ﬂew at Mach 7 (seven times
the speed of sound) for 11.0 seconds. (A scramjet gets its oxygen directly from the air, rather than from fuel.) At this rate, how many minutes would it take such a scramjet to carry passengers the approximately 5000 km from San
1
‘ Francisco to New York? (Use 33] m/sfol' the speed of sound in air.)
i .: t: L'Tffm‘”, """" .......... _; _________________________________ ,,,, _________ ".3 y I (ﬂew [3 htth //session.masteringphysics.com/myct MasteringPhysics 8/20/09 11:00 AM Problem 220 i Description: A test car travels in a straight line along the x axis. The graph in the ﬁgure shows the car’s position x as a
function of time. (:3) Find the x component of instantaneous velocity at point A. (b) Find the x component of instantaneous
g velocity at... 3A test car travels in a Straight line along the I axis. The graph in the ﬁgure shows the car‘s position I as afunction of time. i
i (ml ‘ g
E ., WM. Find the x component of instantaneous velocity at point A. ANSWER: i 6.57, y y l
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; aPartD Find the x component of instantaneous velocity at point D. ANSWER: I KW Part E x i ﬁnd the 3 component of instantaneous velocity at point E. I i ’ ; ANSWER: _400
, W = . E
I Part F a
Find the 1 component of instantaneous velocity at point F. i l E ANSWER: l
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l Find the 1 component of instantaneous velocity at point G. ANSWER: i 0
r 0G: = m/5 l
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l_ Problem 24: Hiking the Paciﬁc Crest Trail. t m X t W Vie,
W a m .. s M ’ Description: The Paciﬁc Crest Trail runs from the Mexican border to the Canadian border through California, Oregon, and
Washington, covering ## miles of trail, but only about ## straightline miles. (a) If you hike this trail in ## weeks. from httpzl/session.masteringphysics.com/myct Page 12 of 14 MasteringPhysics 8/20/09 11:00 AM Mexico to Canada... i
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The Paciﬁc Crest Trail runs from the Mexican border to the Canadian border through California, Oregon, and Washington, i
covering 2650 miles of trail, but only about 1000 straightline miles. §
§
§ Part A 3 t x If you hike this trail in 11.0 weeks, from Mexico to Canada, ﬁnd your average 5%.
; ANSWER: a ‘ / , a; v = M24 mph W V ‘ t WM ilPartB l i
3 E If you hike this trail in 11.0 weeks. from Mexico to Canada, ﬁnd your average velocity ,m i What is your average hiking speed if y0u hike only 7.00 hours per day? l ANSWER: 8
l
l i Problem 2.12 Description: A runner covers one lap of a circular track ## m in diameter in ## s. (a) For that lap, what was her average
speed? (b) For that lap, what was her average velocity? (0) If she covered the ﬁrst half lap in ## 5, what was her average speed for that... A runner covers one lap of a circular track 40.0 m in diameter in 640 5. i i For that lap, what was her average speed? «ANSWERQ 401),: / L , 1 m/s m. If she covered the ﬁrst half —lap in 28.9 5. what was her average speed for that half—lap? ANSWEm; H i v = an 111/8 {damask—W“ If she covered the ﬁrst half lap in 28.9 5, what were her average velocity for that half—lap? : ANSWER:E i y l
l r v = t1 m/s :2
a . Problem 2.14: Ouch! Description: Nerve impulses travel at different speeds, depending on the type of ﬁber through which they move. The impulses
for touch travel at 76.2 m/s, while those registering pain move at 0610 m/s. Assume that person's brain is ## m from his toe ;
and that" Nerve impulses travel at different speeds, depending on the type of ﬁber through which they move. The impulses for touch
travel at 76.2 m/s. while those registering pain move at 0.610 m/s. Assume that person's brain is 1.84 m from his toe and that f httpzl/session.masteringphysics.com/myct Page 13 of 14 MasteringPhysics 8/20/09 11:00 AM if the impulses travel directly from toe to brain. émama If a person stubs his toe, ﬁnd the time for the impulse for touch to reach his brain. ?
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E I ANSWER: h N, t= 6.5—1 5 x
x
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x ' Find the time delay between the pain and touch impulses. ; ANSWERr 1 1
5 h ....._  ....
I At = (0.610 76.2) s Score Summary: Your score on this assignment is 0%
You received 0 out of a possible total of 15 points. http2/lsessionmasteringphysics.com/myct Page 14 of 14 ...
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