PHY111–Chapter1–Problems–Algebra/Trig.Review
5. Newton’s law of universal gravitation is represented by
where F is the gravitational
force, M and m are masses, and r is a length. Force has the SI units of kg*m/s2. What are the SI units of the
proportionalityconstantG?
15.Afathomisaunitoflengthusuallyreservedformeasuringthedepthofwater.Afathomisapproximately6feet
inlength.TakethedistancefromEarthtotheMoontobe250,000miles,andusethegivenapproximationtofindthe
distanceinfathoms.
17.AfirkinisanoldBritishunitofvolumeequalto9gallons.Howmanycubicmetersaretherein6firkins?
19.Acaristravelingataspeedof38.0m/sonaninterstatehighwaywherethespeedlimitis75.0mi/hr.Isthe
driverexceedingthespeedlimit?Justifyyouranswer.
21.Thediameterofasphereismeasuredtobe5.36inches.Find(a)theradiusofthesphereincentimeters,(b)the
surfaceareaofthesphereinsquarecentimeters,and(c)thevolumeofthesphereincubiccentimeters.
23.Thespeedoflightisabout3.00x108m/s.Convertthisfiguretomilesperhour.
25.Theamountofwaterinreservoirsisoftenmeasuredinacre-ft.Oneacre-ftisavolumethatcoversanareaofone
acretoadepthofonefoot.Anacreis43,560ft2.FindthevolumeinSIunitsofareservoircontaining25.0acre-ftof
water.
26.Thebaseofapyramidcoversanareaof13.0acres(1acre=43,560ft2)andhasaheightof481ft.Ifthevolume
ofapyramidisgivenbytheexpressionB=(bh/3),wherebistheareaofthebaseandhistheheight,findthevolume
ofthispyramidincubicmeters.
27. A quart container of ice cream is to be made in the form of a cube. What should be the length of a side, in
centimeters?(Usetheconversion1gallon=3.786liters.)
35. A point is located in a polar coordinate system by the coordinates r = 2.5 m and θ = 350. Find the x- and ycoordinatesofthispoint,assumingthatthetwocoordinatesystemshavethesameorigin.
39. Two points are given in polar coordinates by (r,θ) = (2.00 m, 50.00) and (r,θ) = (5.00 m, –50.00), respectively.
Whatisthedistancebetweenthem?
41.Forthetriangleshowninthefigure,whatare(a)thelengthoftheunknownside,(b)thetangentofθ,and(c)the
sineofϕ?
43.Ahighfountainofwaterislocatedatthecenterofacircularpool,asshownbelow.Notwishingtogethisfeet
wet,astudentwalksaroundthepoolandmeasuresitscircumferencetobe15.0m.Next,thestudentstandsatthe
edgeofthepoolandusesaprotractortogaugetheangleofelevationatthebottomofthefountaintobe55.00.How
highisthefountain?
45.Inthefigurebelow,find(a)thesideoppositeθ,(b)thesideadjacenttoϕ,(c)cosθ,(d)sinϕ,and(e)tanϕ.
48. A woman measures the angle of elevation of a mountaintop as 12.00. After walking 1.00 km closer to the
mountainonlevelground,shefindstheangletobe14.00.(a)Drawapictureoftheproblem,neglectingtheheightof
the woman’s eyes above the ground. Hint: Use two triangles. (b) Select variable names for the mountain height
(suggestion:y)andthewoman’soriginaldistancefromthemountain(suggestion:x)andlabelthepicture.(c)Using
thelabeledpictureandthetangentfunction,writetwotrigonometricequationsrelatingthetwoselectedvariables.
(d) Find the height of the mountain by first solving one equation for x and substituting the result into the other
equation.
49.Asurveyormeasuresthedistanceacrossastraightriverbythefollowingmethod:Startingdirectlyacrossfroma
treeontheoppositebank,hewalksx=100malongtheriverbanktoestablishabaseline.Thenhesightsacrossto
thetree.Theanglefromhisbaselinetothetreeisθ=35.00(seefigure).Howwideistheriver?
53.Onecubiccentimeter(1.0cm3)ofwaterhasamassof1.0x10-3kg=1gram.(a)Determinethemassof1.0m3of
water.Assumingthatbiologicalsubstancesare98%water,estimatethemassesof(b)acellwithadiameterof1.0
μm,(c)ahumankidney,and(d)afly.Takeakidneytoberoughlyaspherewitharadiusof4.0cmandaflytobe
roughlyacylinder4.0mmlongand2.0mmindiameter.
56.Assumethatittakes7.00minutestofilla30.0-gallongasolinetank.(a)Calculatetherateatwhichthetankis
filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c)
Determinethetimeinterval,inhours,requiredtofilla1.0m3volumeatthesamerate.(1USgallon=231in.3)
57.Onegallonofpaint(volume=3.79x10-3m3)coversanareaof25.0m2.Whatisthethicknessofthefreshpainton
thewall?
58.Sphere1hassurfaceareaA1andvolumeV1,andsphere2hassurfaceareaA2andvolumeV2.Iftheradiusof
sphere2isdoubletheradiusofsphere1,whatistheratioof(a)theareas,A2/A1and(b)thevolumes,V2/V1?