479 Horizontal Motion: The horizontal component of velocity ... - Wuala

91962_05_R1_p0479-0512 6/5/09 3:53 PM Page 492
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R1–18. At the instant shown, cars A and B travel at speeds
of 55 mi>h and 40 mi>h, respectively. If B is increasing its
speed by 1200 mi>h 2 , while A maintains its constant speed,
determine the velocity and acceleration of B with respect to
A. Car B moves along a curve having a radius of curvature
of 0.5 mi.
v B 40 mi/h
B
A 30
v A 55 mi/h
v B = -40 cos 30°i + 40 sin 30°j = {-34.64i + 20j} mi>h
v A = {-55i} mi>h
v B>A = v B - v A
= (-34.64i + 20j) - (-55i) = {20.36i + 20j} mi>h
y B>A = 220.36 2 + 20 2 = 28.5 mi>h
u = tan -1 a 20
20.36 b = 44.5° a
Ans.
Ans.
(a B ) n = y2 B
r = 402
0.5 = 3200 mi>h2 (a B ) t = 1200 mi>h 2
a B = (3200 sin 30° - 1200 cos 30°)i + (3200 cos 30° + 1200 sin 30°)j
= {560.77i + 3371.28j} mi>h 2
a A = 0
a B = a A + a B>A
560.77i + 3371.28j = 0 + a B>A
a B>A = {560.77i + 3371.28j} mi>h 2
a B>A = 2(560.77) 2 + (3371.28) 2 = 3418 mi>h 2 = 3.42 A10 3 B mi>h 2
u = tan -1 a 3371.28
560.77 b = 80.6° a
Ans.
Ans.
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