Engineering Mechanics: Dynamics 2e Gray, Costanzo, Plesha
Answers to Selected Even-Numbered Problems
Please note that answers are not provided for the following type of even-numbered problems:
Concept Problems.
Computer Problems.
Design Problems.
For Concept and Computer problems, please consult the solutions manual.
Chapter 1
1.2 .rB=A/` D 3:883 ft
1.4 ErB=A
ˇ
ˇxy system D .4:000 O{ 1:000 O| / ft
ErB=A
ˇ
ˇpq system D .3:313 Oup 2:455 Ouq / ft
ˇ
ˇErB=A
ˇ
ˇxy system D ˇ
ˇErB=A
ˇ
ˇpq system D 4:123 ft
1.6 Ev D .79:68 O{ C 7:190 O| / ft=s
1.8 D 3:229 rad
D 0:087 31 rad
1.10 vr D 504:6 ft=s and v D 353:3 ft=s
1.12 D 101:1ı
1.14 xP 2 D 0:7679 ft and yP 2 D 5:330 ft
1.16 EvA D .20:02 O{ C 12:81 O| / ft=s and EaA D .1:414 O{ C 4:243 O| / ft=s2
1.18 r D 26:36 mm
1.20 ŒIxx ç D ŒIyy ç D ŒI´´ç D ML2
Units of Ixx , Iyy , and I´´ in the SI system: kgm2;
Units of Ixx , Iyy , and I´´ in the U.S. Customary system: slugft2 D lbs2 ft.
1.22 Concept problem.
1.24 the units of E are kg=ms2.
Chapter 2
2.2 Concept Problem
2.4 Concept Problem
1 Last modified: August 16, 2012

Engineering Mechanics: Dynamics 2e Gray, Costanzo, Plesha
2.6 Er1 D 8:747 Our m and Er2 D 13:73 Our m
Evavg

1 D 5:467 Our m=s and Evavg

2 D 8:579 Our m=s
2.8 Ev D .154:0 O{ C 266:7 O| / ft=s
2.10 Ev D .145:4 O{ C 69:81 O| / ft=s
2.12 Ev1 D .0:4623 O{ C 0:08155 O| / m=s
Ev2 D .0:002550 O{ C 0:0004499 O| / m=s
2.14 1 D 12:21ı and 2 D 17:30ı
1 D 102:2ı and 2 D 72:70ı
2.16 .x/ D cos1
3 C 4x
p10 C 24x C 16x2

2.18 Eaavg D .0:04588 O{ C 3:886 O| / ft=s2
Eaavg Ea.5 s/ D .0:001154 O{ 0:003175 O| / ft=s2
2.20 Er D E0
Evavg D E0
d D 1:394 ft
vavg D 0:3485 ft=s
2.22 Computer Problem
2.24 vmax D 2v0 D 58:67 ft=s and vmin D 0 ft=s
yvmin D 0 ft and yvmax D 2R D 2:300 ft
Eavmin D v2
0
R O| D .748:2 ft=s2/ O| and Eavmax D v2
0
R O| D .748:2 ft=s2/ O|
2.26 Rx D 8v2
0 a3
y2 C 4a22
Ry D 4v2
0 a2y
y2 C 4a22
2.28 Ev D .203:2 O{ C 117:3 O| / ft=s
Ea D .27:53 O{ C 47:69 O| / ft=s2
2.30 vmax D 80:82 ft=s
2.32 Ev D .51:32 O{ 1:046 O| / ft=s
Ea D .0:3873 O{ C 19:00 O| / ft=s2
2 Last modified: August 16, 2012

Engineering Mechanics: Dynamics 2e Gray, Costanzo, Plesha
2.34 v D !
p
d 2 x2
s
1 C h2
x
d 2 x3
d 4
2
v D 0:5236 ft=s; v D 0:4554 ft=s; and v D 0
2.36 EvA D .72:00 O{ C 96:00 O| / ft=s
EaA D .460:8 O{ 345:6 O| / ft=s2
2.38 Computer Problem
2.40 tbraking D 7:854 s
2.42 jajmax D 3:600 m=s2
tjamaxj

1 D 3:927 s and tjamaxj

2 D 11:78 s
sjamaxj

1 D 12:84 m and sjamaxj

2 D 128:5 m
2.44 Largest distance traveled in 1 s is d D 0:2667 m, corresponding to a D ˇ1
pt
2.46 v.0/ D 0:080 00 ft=s
2.48 v0 D 10:10 m=s
2.50 ac D 22:36 g
2.52 tstop D 2:880 s
2.54 D 98:10 s1
2.56 Px D ˚7:000 sinŒ.1:000 rad=s/tç C 10:50 cosŒ.0:5000 rad=s/tç 10:50 m=s
x D ˚7:000 7:000 cosŒ.1:000 rad=s/tç C 21:00 sinŒ.0:5000 rad=s/tç .10:50 s1/t m=s2
2.58 tstop D 0:2233 s
2.60 vterm D 4:998 m=s
2.62 jvjmax D 1:128 m=s
sjvjmax D 0:1250 m and sjvjmax D 0:1250 m
2.64 v.t/ D mg
Cd

1 eCd t=m
vterm D mg
Cd
2.66 vf D 3:563 m=s
2.68 Computer Problem
3 Last modified: August 16, 2012

Engineering Mechanics: Dynamics 2e Gray, Costanzo, Plesha
2.70 swet D 26:31 m
.swet sdry/
sdry
.100%/ D 65:21%
2.72 P./ D ˙
r
P2
0 C 2 g
L
cos cos 0

2.74 Pmin D 4:930 rad=s
2.76 Px D ˙
s
v2
0 C 2

g C kL0
m

.x x0/ k
m
x2 x2
0

2.78 txmax D 0:2433 s
2.80 (a) Pr D p2G .mA C mB /
r r0 r
rr0
(b) (i) Pr D 5:980 105 ft=s and (ii) Pr ! 1
2.82 Concept Problem
2.84 d D 186:4 ft
2.86 ˛s D ap
r C hv2
p
2 r3
˛s
ˇ
ˇrDr1 D 1:442 rad=s2 and ˛s
ˇ
ˇrDr2 D 3:631 rad=s2
2.88 v D v0 C ac .t t0/
s D s0 C v0.t t0/ C 1
2 ac .t t0/2
2.90 vmin D 113:5 ft=s
2.92 ti D 3:497 s
EvB D .33:33 O{ 34:31 O| / m=s
2.94 R D 5:047 m
2.96 tflight D 6:263 s
Erland D .281:8 O{ 4:500 O| / m
2.98 d D 24:09 m
2.100 (a) Rmax D
4 rad D 45ı
(b) Rmax D 233:5% of the actual maximum range
(c) tRmax D 119:5 s
2.102 1 D 1
2 sin1.gR=v2
0 / and 2 D 90ı 1
2 sin1.gR=v2
0 /
1 D 24:86ı and 2 D 65:14ı
4 Last modified: August 16, 2012

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Solution Manual for Engineering Mechanics: Dynamics, 2nd Edition

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