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Problem 1
Suppose, a lighthouse operator (L) observes a shipping boat (B) that is moving straight away from
the light house. The level of the lighthouse operator is 20 m above the level of the sea. At a
particular instant, the lighthouse operator observe the boat (B1 ) with a depression angle of 800 .
Two minutes later, the boat (B2 ) was observed with a depression angle of 400 . What is vB , the
speed of the boat as measured by the light house operator in m/s?
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Problem 2
The vectors ~u and ~v are given such that ~u =< 3 − 1 2 >, and ~v =< −2 0 1 >. Find the unit vector
n̂ in the direction of ~u × ~v .
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Problem 3
An 80 kg (176 lb) climber(C) is moving, vertically up, along the rope(R). At each grip, the climber
receives a vertical acceleration of magnitude 0.5 m/s2 . Applying appropriate Newton’s laws, determine, |F~T (R,C |, the magnitude of the force of tension from the rope on the climber!
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Problem 4
A spherical helium filled balloon (B) with a hanging passenger cage being held by a single vertical
cable (C) attached to Earth (Cable is going from the cage to ground). If the total mass of the
balloon and the cage is 200 kg and the radius of the balloon is 5 m, how much tension (at least),
the cable could be able to support in order to keep the balloon from breaking away. (Density of
air is approximately 1.225 kg/m3 .)
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Problem 5
Suppose an piece of rock was thrown horizontally from the first floor balcony of a building. The
stone landed on the flat ground 15 m away from the balcony. Assume the balcony level is 3 m
above the level flat ground. Ignore the effects from air on the piece of rock. What was the speed
at which the piece of rock was shot out?
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Problem 6
Stunt biker Danny MacAskill (D) rides his bicycle in a vertical loop of radius 2.5 m inside a concrete
cylinder (C). Danny is able to change the speed while taking the loop. Suppose, Danny passes the
bottom point of the loop at the speed 10 m/s. Together, the mass of Danny and the bike is 70 kg.
• For the scope of this problem, suppose, Danny moves inside the cylinder continuosly without
trying to escape.
a). What is the magnitude of F~N (C,D) , the normal force from the cylinder on Danny and the
bike, when they pass the bottom of the cylinder?
b). If Danny manages to receive the same normal force throughout the loop by adjusting his
speed, what should be his speed when he passes the top of the cylinder?
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Problem 7
After applying breaks to stop at a stop sign, a 1000 kg car (C) skids (wheels are locked) along the
straight flat road (R) for a halt. The car was initially traveling at 15 m/s and it was brought to a
complete stop within 3 seconds. Assume, no air resistance.
i. Using a force diagram and the definition of the work done, identify if each force does positive,
negative, or zero work on the system of the “car and the passengers”.
ii. Apply work-energy principle to determine the total work done by external forces in stopping
the car.
iii. What force is responsible for this work?
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Problem 8
Figure skater Elena Sokolova spins at 6.00 rev/s keeping her arms closer to maintain a moment
of inertia of 0.400 kg m2 . She manages to stand on the toe of one feet to minimize her contact
with ice surface. Next she reduces her rate of spinning (angular velocity) by extending her arms to
increase the moment of inertia. Then her rate of spinnig decreased to 4 rev/sec.
a) Determine the moment of inertia of Elena when she extend her arms
b) If Elena kept her arms in, and increased her contact with the surface to allow friction from
ice to slow her down to 3.00 rev/s with in 15 s, then determine the average torque applied by
friction from ice on Elena.
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