- You are watching a National Geographic Special on
television. One segment of the program is about archer
fish, which inhabit streams in southeast Asia. This fish
actually "shoots" water at insects to knock
them into the water so it can eat them. The commentator
states that the archer fish keeps its mouth at the
surface of the stream and squirts a jet of water from its
mouth at 13 feet/second. You watch an archer fish shoot a
juicy moth off a leaf into the water. You estimate that
the leaf was about 2.5 feet above a stream. You wonder at
what minimum angle from the horizontal the water can be
ejected from the fish's mouth to hit the moth. Since you
have time during the commercial, you quickly calculate
this angle.

- Your artist friend is designing a kinetic sculpture and
asks for your help since she knows that you have had
physics. Part of her sculpture consists of a 6.0-kg
object (you can't tell what it is supposed to be, but
it's art) and a 4.0-kg object which hang straight down
from opposite ends of a very thin, flexible wire. This
wire passes over a smooth, cylindrical, horizontal,
stainless steel pipe 3.0 meters above the floor. The
frictional force between the rod and the wire is
negligible. The 6.0-kg object is held 2.0 meters above
the floor and the other object hangs 0.50 meters above
the floor. When the mechanism releases the 6.0-kg object,
both objects accelerate and one will eventually hit the
floor -- but they don't hit each other. To determine if
the floor will be damaged, calculate the speed of the
object which hits the floor.

- You are driving your car uphill along a straight road.
Suddenly, you see a car run a red light and enter the
intersection just ahead of you. You slam on your brakes
and skid in a straight line to a stop, leaving skid marks
100 feet long. A policeman observes the whole incident
and gives a ticket to the other car for running a red
light. He also gives you a ticket for exceeding the speed
limit of 30 mph. When you get home, you read your physics
book and estimate that the coefficient of kinetic
friction between your tires and the road was 0.60, and
the coefficient of static friction was 0.80. You estimate
that the hill made an angle of about 10owith the
horizontal. You look in your owner's manual and find that
your car weighs 2,050 lbs. Will you fight the traffic
ticket in court?

- You have landed a summer job with a company that has been
given the contract to design the ski jump for the next
Winter Olympics. The track is coated with snow and has an
angle of 25o from the horizontal. A skier zips down the
ski jump ramp so that he leaves it at high speed. The
winner is the person who jumps the farthest after leaving
the end of the ramp. Your task is to determine the height
of the starting gate above the end of the ramp, which
will determine the mechanical structure of the ski jump
facility. You have been told that the typical ski-jumper
pushes off from the starting gate at a speed of 2.0 m/s.
For safety reasons, your design should be such that for a
perfect run down the ramp, the skier's speed before
leaving the end of the ramp and sailing through the air
should be no more than 80 km/hr. You run some experiments
on various skies used by the jumpers and determine that
the coefficient of static friction between the snow and
the skis is 0.10 and its coefficient of kinetic friction
is 0.02. Since the ski-jumpers bend over and wear very
aerodynamic suits, you decide to neglect the air
resistance to make your design.

- The Navy wants a new airplane launcher for their aircraft
carriers that is basically a large spring and your job is to determine
the necessary spring constant. The launcher pushes the plane for a short
distance along a much longer runway. During that same time, the plane's
jet engines supply a constant thrust force for the entire length of the
runway. The planes need to have a minimum velocity by the time they
reach the end of the runway in order to take off successfully.

- You have been hired to design a safety system to protect
drivers going down hills during an ice storm. The planned
system consists of a bumper, which can be considered a
stiff spring, at the bottom of the hill. In the scenario
you are given, the car starts from rest at the top of a
hill which makes an angle q with the horizontal. The
distance that the car slides from the top of the hill
until it is stopped by the spring is L. For the worst
case scenario, assume that there is no frictional force
between the car and road due to the ice. If the maximum
compression of the spring from its equilibrium position
is D, your job is to calculate the required spring
constant k in terms of D, L and q.

- You work for the National Park Service testing a small cannon
used to prevent avalanches by shooting down snow overhanging the sides
of mountains. In order to determine the range of the cannon, it is
necessary to know the speed with which the projectile leaves the cannon
(muzzle speed), relative to the ground. The cannon you are testing has
a weight of 500 lbs. and shoots a 20-lb. projectile. During lab tests
where the cannon is held and cannot move, the muzzle speed is 400 m/s.
You want to calculate the projectile's muzzle speed with respect to the
ground under field conditions when the cannon is mounted so that it is
free to move (recoil) when fired. You take the case where the cannon is
fired horizontally using the same shells as in the laboratory.

- Super Dave has just returned from the hospital where he
spent a week convalescing from injuries incurred when he
was "shot" out of a cannon to land in an airbag
which was too thin. Undaunted, he decides to celebrate
his return with a new stunt. He intends to jump off a
100-foot tall tower with an elastic cord tied to one
ankle, and the other end tied to the top of the tower.
This cord is very light but very strong and stretches so
that it can stop him without pulling his leg off. Such a
cord exerts a force with the same mathematical form as
the spring force. He wants it to be 75 feet long so that
he will be in free fall for 75 feet before the cord
begins to stretch. To minimize the force that the cord
exerts on his leg, he wants it to stretch as far as
possible. You have been assigned to purchase the cord for
the stunt and must determine the elastic force constant
which characterizes the cord that you should order.
Before the calculation, you carefully measure Dave's
height to be 6.0 ft and his weight to be 170 lbs. For
maximum dramatic effect, his jump will be off a diving
board at the top of the tower. From tests you have made,
you determine that his maximum speed coming off the
diving board is 10 ft/sec. Neglect air resistance in your
calculation -- let Dave worry about that.

- As part of a fundraiser, you want the new dean to bungee jump
from a crane. The jump will be made from 44 m above a 2.5 m deep pool of
Jello. A 30 m long bungee cord would be attached to the dean's ankle.
You must convince the dean that your plan is safe for a person of his
mass, 70 kg. As the bungee cord stretches, it will exert a force with
the same properties as the force exerted by a spring. Your plan has the
dean stepping off a platform and being in free fall for the 30 m before
the cord begins to stretch. You must determine the elastic constant of
the bungee cord so that it stretches only 12 m, which will keep the
dean's head just out of the Jello.

- Your artist friend's new work is a simple, high-impact kinetic
sculpture called 'Destruction.' A 200-kg steel block is hung from the
ceiling by an 8-foot-long rope. A second rope is attached to the side
of the block. The other end of this second rope is attached to a motor
which is cleverly mounted so that the rope always pulls the block
horizontally with a constant force. The block starts from rest, hanging
straight down, and is pulled slowly by the motor until it is hanging at
an angle of 30 degrees from the vertical. The horizontal rope is then released
and the block swings and crashes into a wall. Your friend knows you
have taken physics and asks you the minimum energy that the motor must
supply. You perform a test and determine that the block is in
equilibrium when it has been pulled so that it hangs at 30 degrees from
the vertical.

- (Gravitational Energy) Because of your knowledge of
physics and interest in the environment, you have gotten
a summer job with an organization which wants to orbit a
satellite to monitor the amount of chlorine ions in the
upper atmosphere over North America. It has been
determined that the satellite should collect samples at a
height of 100 miles above the Earth's surface.
Unfortunately, at that height air resistance would make
the amount of time the satellite would stay in orbit too
short to be useful. You suggest that an elliptical orbit
would allow the satellite to be close to the Earth over
North America, where data was desired, but farther from
the Earth, and thus out of almost all of the atmosphere,
on the other side of our planet. Your colleague estimates
that the satellite would be traveling at 10,000
miles/hour when it was farthest from the Earth at a
height of 1,000 miles. How fast would the satellite be
traveling when it took its air samples if you neglect air
friction?

- At the train station, you notice a large horizontal spring at
the end of the track where the train comes in. This is a safety device
to stop the train so that it will not plow through the station if the
engineer misjudges the stopping distance. While waiting, you wonder what
would be the fastest train that the spring could stop at its full
compression, 3.0 ft. To keep the passengers safe when the train stops,
you assume a maximum stopping acceleration of g/2. You also guess that a
train weighs half a million lbs. For purpose of getting an estimate, you
decide to assume that all frictional force are negligible.

- Your company is designing an apparatus for an ice skating show.
An ice skater will start from rest and slide down an ice-covered ramp.
At the bottom of the ramp, the skater will glide around an ice-covered
loop which is the inside of a vertical circle before emerging out onto
the skating rink floor. For a spectacular effect, the circular loop will
have a diameter of 30 feet. Your task is to determine the minimum height
from the rink floor to the top of the ramp for the skater to make it
around the loop. When barely making it around, the skater briefly loses
contact with the ice at the top of the loop and at that point the skater
is in free fall.

- In a weak moment you have volunteered to be a human
cannonball at an amateur charity circus. The
"cannon" is actually a 3-foot diameter tube
with a big stiff spring inside which is attached to the
bottom of the tube. A small seat is attached to the free
end of the spring. The ringmaster, one of your soon to be
ex-friends, gives you your instructions. He tells you
that just before you enter the mouth of the cannon, a
motor will compress the spring to 1/10 its normal length
and hold it in that position. You are to gracefully crawl
in the tube and sit calmly in the seat without holding on
to anything. The cannon will then be raised to an angle
such that your speed through the air at your highest
point is 10 ft/sec. When the spring is released, neither
the spring nor the chair will touch the sides of the
12-foot long tube. After the drum roll, the spring is
released and you will fly through the air with the
appropriate sound effects and smoke. With the perfect aim
of your gun crew, you will fly through the air over a
15-foot wall and land safely in the net. You are just a
bit worried and decide to calculate how high above your
starting position you will be at your highest point.
Before the rehearsal, the cannon is taken apart for
maintenance. You see the spring, which is now removed
from the cannon, is hanging straight down with one end
attached to the ceiling. You determine that it is 10 feet
long. When you hang on its free end without touching the
ground, it stretches by 2.0 ft. Is it possible for you to
make it over the wall?

- You are on a committee investigating injuries to students
participating in sports, starting with the high incidence of ankle
injuries on the basketball team. Observing the team practice jump shots
inspires you to try a small calculation. A 50-kg student jumps 1.0 meter
straight up and shoots the 0.80-kg basketball at the top of the jump.
From the path of the basketball, you estimate that the ball left the
hand at 30 degrees from the horizontal at 5 m/s. To determine the horizontal
forces on the ankle, you decide to calculate the student's horizontal
velocity when hitting the ground.

- Because of your interest in the environment and your physics
experience, you have been asked by the Campus Museum of Natural History
to assist in the production of an animated film about hawks. In the
script, a 1.5-kg hawk hovers motionless with respect to the ground when
it sees a goose flying below it. The hawk dives straight down. It
strikes the goose at a speed of 60 km/hr and digs its claws into the
goose's body. The 2.5 kg goose was flying north at 30 km/hr just before
it was struck by the hawk and killed instantly. The animators want to
know the velocity of the hawk and dead goose just after the strike.

- As part of an interview for a summer job with the Coast Guard,
you are asked to help determine the search area for two sunken ships by
calculating their velocity just after they collided. According to the
last radio transmission from the 40,000-ton luxury liner, the Hedonist,
it was going due west at a speed of 20 knots in calm seas through a rare
fog just before it was struck broadside by the 60,000-ton freighter, the
Ironhorse, which was traveling north at 10 knots. The transmission also
noted that when the freighter's bow pierced the hull of the liner, the
two ships stuck together and sank together.

- You have been hired to check the technical correctness of an
upcoming made-for-TV murder mystery that takes place in the space
shuttle. In one scene, an astronaut's safety line is cut while on a
space walk. The astronaut, who is 200 meters from the shuttle and not
moving with respect to it, finds that the suit's thruster pack has also
been damaged and no longer works and that only 4 minutes of air remains.
To get back to the shuttle, the astronaut unstraps a 10-kg tool kit and
throws it away with a speed of 8 m/s. In the script, the astronaut, who
has a mass of 80 kg without the toolkit, survives, but is this correct?

- You have been hired as a technical consultant for an
early-morning cartoon series for children to make sure
that the science is correct. In the script, a wagon
containing two boxes of gold (total mass of 150 kg) has
been cut loose from the horses by an outlaw. The wagon
starts from rest 50 meters up a hill with a 6o slope. The
outlaw plans to have the wagon roll down the hill and
across the level ground and then crash into a canyon
where his confederates wait. But in a tree 40 meters from
the edge of the canyon wait the Lone Ranger (mass 80 kg)
and Tonto (mass 70 kg). They drop vertically into the
wagon as it passes beneath them. The script states that
it takes the Lone Ranger and Tonto 5 seconds to grab the
gold and jump out of the wagon, but is this correct?. You
assume that the wagon rolls with negligible friction.

- You are helping your friend prepare for the next skateboard
exhibition by determining if the planned program will work. Your friend
will take a running start and then jump onto a heavy-duty 15-lb
stationary skateboard. The skateboard will glide in a straight line
along a short, level section of track, then up a sloped concrete wall.
The goal is to reach a height of at least 10 feet above the starting
point before coming back down the slope. Your friend's maximum running
speed to safely jump on the skateboard is 23 feet/second. Your friend
weighs 150 lbs.

- Because of your physics background, you have been hired
as a technical advisor for a new James Bond adventure
movie. In the script, Bond and his latest love interest,
who is 2/3 his weight (including skis, boots, clothes,
and various hidden weapons), are skiing in the Swiss
Alps. She skis down a slope while he stays at the top to
adjust his boot. When she has skied down a vertical
distance of 100 ft, she stops to wait for him and is
captured by the bad guys. Bond looks up and sees what is
happening. He notices that she is standing with her skis
pointed downhill while she rests on her poles. To make as
little noise as possible, Bond starts from rest and
glides down the slope heading right at her. Just before
they collide, she sees him coming and lets go of her
poles. He grabs her and they both continue downhill
together. At the bottom of the hill, another slope goes
uphill and they continue to glide up that slope until
they reach the top of the hill and are safe. The writers
want you to calculate the maximum possible height that
the second hill can be relative to the position where the
collision took place. Both Bond and his girl friend are
using new, top-secret frictionless stealth skis developed
for the British Secret Service.

- Because of your concern that incorrect science is being
taught to children when they watch cartoons on TV, you
have joined a committee which is reviewing a new cartoon
version of Tarzan. In this episode, Tarzan is on the
ground in front of a herd of stampeding elephants. Just
in time Jane, who is up in a tall tree, sees him. She
grabs a convenient vine and swings towards Tarzan, who
has twice her mass, to save him. Luckily, the lowest
point of her swing is just where Tarzan is standing. When
she reaches him, he grabs her and the vine. They both
continue to swing to safety over the elephants up to a
height which looks to be about 1/2 that of Jane's
original position. To decide if you going to approve this
cartoon, calculate the maximum height Tarzan and Jane can
swing as a fraction of her initial height.

- You are watching a Saturday morning cartoon concerning a
jungle hero called George of the Jungle. George attempts
to save his friend, an ape named Ape, from a stampeding
herd of wildebeests. Ape is at the base of a tall tree
which has a vine attached to its top. George is in
another tree holding the other end of the vine. George
plans to swing down from the tree, grab Ape at the bottom
of the swing, and continue up to safety on a ledge which
is half of George's initial height in the tree. Assuming
that Ape weighs the same as George, will they
successfully make it to the top of the ledge?

- Your friend has just been in a traffic accident and hopes that
you can show the accident was the other drivers fault. Your friends
car was traveling North when it entered the intersection. When it
reached the center of the intersection, the car was struck by the other
drivers car which was traveling East. The two cars remained joined
together after the collision and skidded to a stop. The speed limit on
both roads is 50 mph. From the skid marks still visible on the street,
you determine that after the collision the cars skidded 56 feet at an
angle of 30 degrees north of east before stopping. The police report gives the
make and year of each car. The weight of your friends car is 2600 lbs
and that of the other car is 2200 lbs, including the drivers weight in
each case. The coefficient of kinetic friction for a rubber tire
skidding on dry pavement is 0.80. You decide to see if the other driver
was speeding and if your friend was under the speed limit.

- Because movie producers have come under pressure for
teaching children incorrect science, you have been
appointed to help a committee of concerned parents review
a script for a new Superman movie. In the scene under
consideration, Superman rushes to save Lois Lane who has
been pushed from a window 300 feet above a crowded
street. Superman is 0.5 miles away when he hears Lois
scream and rushes to save her. He swoops down in the nick
of time, arriving when Lois is just 3.0 feet above the
street, and stopping her just at ground level. Lois
changes her expression from one of horror at her
impending doom to a smile of gratitude as she gently
floats to the ground in Superman's arms. The committee
wants to know if there is really enough time to express
this range of emotions, even if there is a possible
academy award on the line. The chairman asks you to
calculate the time it takes for Superman to stop Lois's
fall. To do the calculation, you assume that Superman
applies a constant force to Lois in breaking her fall and
that she weighs 120 lbs. While thinking about this scene
you also wonder if Lois could survive the force that
Superman applies to her.

- This year you have a summer job working for the National
Park Service. Since they know that you have taken
physics, they start you off in the laboratory which tests
possible new equipment. Your first job is to test a small
cannon. During the winter, small cannons are used to
prevent avalanches in populated areas by shooting down
heavy snow concentrations overhanging the sides of
mountains. In order to determine the range of the cannon,
it is necessary to know the velocity with which the
projectile leaves the cannon (muzzle velocity). The
cannon you are testing has a weight of 700 lbs and shoots
a 40-lb projectile. During the lab tests the cannon is
held horizontally in a rigid support so that it cannot
move. Under those conditions, you measure the magnitude
of the muzzle velocity to be 400 m/s. When the cannon is
actually used in the field, however, it is mounted so
that it is free to move (recoil) when it is fired. Your
boss asks you to calculate the projectile's speed leaving
the cannon under field conditions, when it is allowed to
recoil. She tells you to take the case where the cannon
is fired horizontally using cannon shells which are
identical to those used in the laboratory test.

- For a part time job with a medical physics group, you are
studying a cancer therapy that uses neutrons to knock a particle out of
the nucleus of the atoms of cancer cells. This is an inelastic collision
in which the heavy nucleus essentially does not move. After the
collision, the nucleus decays and kills the cancer cell. You decide to
measure the change in internal energy of a nitrogen nucleus after a
neutron collides with it. In the experiment, a neutron hits the nucleus
with a speed of 2.0 x 10^7 m/s and you detect two neutrons both coming
out at angles of 30 degrees with respect to the direction that the neutron
coming in.