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Unformatted text preview: Physics 171.101 Exam 1 answers Feb. 24, 2005
Prof. Barnett Do all problems. Everything should be written in ink.
You are allowed to use a calculator and material written on one 3”x5” index card. Use Sin(37°):Cos(53°):0.6, Cos(37°):Sin(530)=0.8, g = 10 m/sz. 1. Two vectors fl and I; have magnitudes of 20 and 10 respectively. Vector X makes
an angle of +530 with respect to the X axis. Vector B makes an angle of +370 with respect to the X axis. A) (10 pts)AWrite each vector, 21 and g,
in i,j,lg notation. A
A212i+16j 8i+6j. B) (10 pts) Evaluate B. 192.0
C) (10 pts) Evaluate >< 0.0 E
g. 2. A large ferris wheel is operating at a fair. The distance from its center to each chair
is 10 meters. The speed of each chair as the wheel turns in the clockwise direction is
5 m / sec. The center of the ferris wheel is 11 meters from the ground. Suddenly, a nut
comes off of a chair which is rising on the rear of the wheel and is oriented at 37" to
the horizontal as illustrated in the diagram below. For uniformity, let’s deﬁne the axis of the ferris wheel as the origin with the “+X” direction to the right and the “+Y”
direction as up. Use 2', j, k notation consistent with this coordinate system deﬁnition. A) (5 pts) What is the angular velocity, (3,
of the ferris wheel? —— 0.5/sec k B) (5 pts) What is the location, R'Wlease), of the
nut just as it releases from the chair? (—8; — meters
C) (5 pts) What is the linear velocity, 1706161135),
of the nut just as it releases from the chair?
(—373 + 4j) m/sec
D) (8 pts) How much time passes from when the nut releases and it lands on the ground?
Use 9 = 10 m/secz. 1.48 seconds. E) (7 pts) At what point, gnawing), does the nut
land on the ground? (—12.43? — 11j)meters F) (5 pts) What is the velocity, ﬁaandmg), of the nut when it lands on the ground?
(—32 — 10.83) m/s'ec. G) (5 pts) What is the speed, Saundmg), of the nut when it lands on the ground?
11.2 m/sec. TURN PAGE OVER 3. Romeo and Juliet are on opposite sides of a river. The river is 1.6 miles wide. Juliet is
somewhat downstream from Romeo so that when he looks toward her his line of sight
makes an angle of 37" relative to a. line directly across the river. Romeo gets into a
row boat and rows across the river always traveling directly toward Juliet. He arrives
very exhausted next to Juliet after rowing for 15 minutes. Deﬁne “+X” as across the river and “+Y” as downstream from Romeo toward Juliet. A) (5 pts) How far downstream is Juliet relative to Romeo? 1.2 miles B) (5 pts) How far does Romeo travel during the 15 minute trip across the river?
2.0 miles. C) (5 pts) What is Romeo’s velocity, QRomeo to ground), during the trip?
(6.42 + 4.83) miles/hour. It happens that the river has a speed, Shiver to ground), of 10 miles per hour downstream
during Romeo’s trip. D) (8 pts) At what angle must he aim his boat
relative to the river during the trip? Romeo
Draw a diagram making this angle clear, '
i.e. showing whether he must aim somewhat
“upstream” or somewhat “downstream”. 39.10 upstream. E) (7 pts) What must Romeo’s speed, Smomeo to river),
be relative to the river during the trip? 8.25 miles / hour i 3 +X +Y’ ...
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- Fall '08