# Unit 1 Kinematics

```Unit 1
Kinematics
1 - Walking the Dog
You and your dog go for a walk to the park.
On the way, your dog takes many side trips
1) yes
to chase squirrels or examine fire hydrants.
When you arrive at the park, do you and
your dog have the same displacement?
2) no
1 - Walking the Dog
You and your dog go for a walk to the park.
On the way, your dog takes many side trips
1) yes
to chase squirrels or examine fire hydrants.
When you arrive at the park, do you and
2) no
your dog have the same displacement?
Yes, you have the same displacement. Since you and your dog had the
same initial position and the same final position, then you have (by
definition) the same displacement.
Follow-up: Have you and your dog traveled the same distance?
2 - Displacement
Does the displacement of an object
depend on the specific location of the
1) yes
2) no
3) it depends on the
origin of the coordinate system?
coordinate system
2 - Displacement
Does the displacement of an object
1) yes
depend on the specific location of the
2) no
origin of the coordinate system?
3) it depends on the
coordinate system
Since the displacement is the
difference between two
1
0
2
0
3
0
4
0
5
0
3
0
4
0
5
0
6
0
7
0
coordinates, the origin does not
matter.
3 - Position and Speed
1) yes
If the position of a car is zero,
2) no
does its speed have to be
3) it depends on the
zero?
position
3 - Position and Speed
1) yes
If the position of a car is zero,
2) no
does its speed have to be
3) it depends on the
zero?
position
No, the speed does not depend on position, it depends on the change of
position. Since we know that the displacement does not depend on the origin of
the coordinate system, an object can easily start at x = –3 and be moving by the
time it gets to x = 0.
4 - Odometer
Does the odometer in a car
1) distance
measure distance or
2) displacement
displacement?
3) both
4 - Odometer
Does the odometer in a car
1) distance
measure distance or
2) displacement
displacement?
3) both
If you go on a long trip and then return home, your odometer does not
measure zero, but it records the total miles that you traveled. That means the
odometer records distance.
Follow-up: How would you measure displacement in your car?
5 - Speedometer
Does the speedometer in a car
measure velocity or speed?
1) velocity
2) speed
3) both
4) neither
5 - Speedometer
Does the speedometer in a car
measure velocity or speed?
1) velocity
2) speed
3) both
4) neither
The speedometer clearly measures speed, not velocity. Velocity is a vector
(depends on direction), but the speedometer does not care what direction you
are traveling. It only measures the magnitude of the velocity, which is the
speed.
Follow-up: How would you measure velocity in your car?
6 - Acceleration I
1) yes
If the velocity of a car is non-zero (v ≠0),
2) no
can the acceleration of the car be zero?
3) depends on the
velocity
6 - Acceleration I
1) yes
If the velocity of a car is non-zero (v≠ 0),
2) no
can the acceleration of the car be zero?
3) depends on the
velocity
Sure it can! An object moving with constant velocity has a
non-zero velocity, but it has zero acceleration since the
velocity is not changing.
7 - Acceleration II
When throwing a ball straight up,
which of the following is true about
1) both v = 0 and a = 0
2) v ≠ 0, but a = 0
3) v = 0, but a ≠ 0
its velocity v and its acceleration a at
4) both v ≠0 and a ≠ 0
the highest point in its path?
5) not really sure
7 - Acceleration II
When throwing a ball straight up,
1) both v = 0 and a = 0
which of the following is true about
2) v ≠ 0, but a = 0
its velocity v and its acceleration a at
3) v = 0, but a ≠ 0
4) both v ≠0 and a ≠ 0
the highest point in its path?
5) not really sure
At the top, clearly v = 0 because the ball has
momentarily stopped. But the velocity of the ball is
changing, so its acceleration is definitely not zero!
Otherwise it would remain at rest!!
Follow-up: …and the value of a is…?
y
8 - Free Fall I
You throw a ball straight up
into the air. After it leaves
your hand, at what point in
its flight does it have the
maximum value of
acceleration?
1) its acceleration is constant
everywhere
2) at the top of its trajectory
3) halfway to the top of its trajectory
4) just after it leaves your hand
5) just before it returns to your hand
on the way down
8 - Free Fall I
You throw a ball straight up
1) its acceleration is constant
into the air. After it leaves
everywhere
your hand, at what point in
2) at the top of its trajectory
its flight does it have the
3) halfway to the top of its trajectory
maximum value of
4) just after it leaves your hand
acceleration?
5) just before it returns to your hand
on the way down
The ball is in free fall once it is released. Therefore, it is entirely under the
influence of gravity, and the only acceleration it experiences is g, which is
constant at all points.
9 - Free Fall II
Alice and Bill are at the top of a
1) Alice’s ball
building. Alice throws her ball
2) it depends on how hard
downward. Bill simply drops his
the ball was thrown
ball. Which ball has the greater
3) neither -- they both have
acceleration just after release?
the same acceleration
4) Bill’s ball
Alice
v
Bill
0
v
v
A
B
9 - Free Fall II
Alice and Bill are at the top of a
1) Alice’s ball
building. Alice throws her ball
2) it depends on how hard
downward. Bill simply drops his
the ball was thrown
ball. Which ball has the greater
3) neither -- they both have
acceleration just after release?
the same acceleration
4) Bill’s ball
therefore they both feel the acceleration due to
Alice
v
gravity (g). This acceleration is independent of the
0
Both balls are in free fall once they are released,
initial velocity of the ball.
v
v
A
B
Follow-up: Which one has the greater velocity when they hit
the ground?
Bill
10 - Up in the Air I
You throw a ball upward with an
initial speed of 10 m/s. Assuming
1) more than 10 m/s
2) 10 m/s
3) less than 10 m/s
that there is no air resistance,
what is its speed when it returns
to you?
4) zero
10 - Up in the Air I
You throw a ball upward with an
initial speed of 10 m/s. Assuming
1) more than 10 m/s
2) 10 m/s
that there is no air resistance,
3) less than 10 m/s
what is its speed when it returns
4) zero
to you?
The ball is slowing down on the way up due to gravity.
Eventually it stops. Then it accelerates downward due to
gravity (again). Since a = g on the way up and on the way
down, the ball reaches the same speed when it gets back
to you as it had when it left.
11 - Up in the Air II
Alice and Bill are at the top of a cliff of height
1) vA < vB
H. Both throw a ball with initial speed v0,
Alice straight down and Bill straight up. The
2) vA = vB
speeds of the balls when they hit the ground
3) vA > vB
are vA and vB. If there is no air resistance,
4) impossible to tell
which is true?
Alice v
0
v
Bill
H
0
v
v
A
B
11 - Up in the Air II
Alice and Bill are at the top of a cliff of height
H. Both throw a ball with initial speed v0, Alice
1) vA < vB
straight down and Bill straight up. The speeds
2) vA = vB
of the balls when they hit the ground are vA
3) vA > vB
and vB. If there is no air resistance, which is
4) impossible to tell
true?
Bill’s ball goes up and comes back down
downward with v0, the same as Alice’s
Alice v
0
v
ball. Thus, it will hit the ground with the
0
same speed as Alice’s ball.
v
v
A
B
to Bill’s level. At that point, it is moving
Bill
H
Follow-up: What happens if there is air resistance?
12 - Throwing Rocks I
You drop a rock off a
bridge. When the rock has
fallen 4 m, you drop a
second rock. As the two
rocks continue to fall, what
happens to their
separation?
1) the separation increases as they fall
2) the separation stays constant at 4 m
3) the separation decreases as they fall
4) it is impossible to answer without more
information
12 - Throwing Rocks I
You drop a rock off a bridge.
1) the separation increases as they fall
When the rock has fallen 4
m, you drop a second rock.
2) the separation stays constant at 4 m
As the two rocks continue to
3) the separation decreases as they fall
fall, what happens to their
4) it is impossible to answer without more
separation?
information
At any given time, the first rock always has a greater velocity than the
second rock, therefore it will always be increasing its lead as it falls.
Thus, the separation will increase.
13 - Throwing Rocks II
You drop a rock off a
1) both increase at the same rate
bridge. When the rock has 2) the velocity of the first rock increases faster
fallen 4 m, you drop a
than the velocity of the second
second rock. As the two
3) the velocity of the second rock increases
rocks continue to fall, what faster than the velocity of the first
happens to their
velocities?
4) both velocities stay constant
13 - Throwing Rocks II
You drop a rock off a
1) both increase at the same rate
bridge. When the rock has
fallen 4 m, you drop a
second rock. As the two
rocks continue to fall, what
happens to their
velocities?
2) the velocity of the first rock increases faster
than the velocity of the second
3) the velocity of the second rock increases
faster than the velocity of the first
4) both velocities stay constant
Both rocks are in free fall, thus under the influence of gravity only. That means
they both experience the constant acceleration of gravity. Since acceleration is
defined as the change of velocity, both of their velocities increase at the same
rate.
Follow-up: What happens when air resistance is present?
14 - Graphing Velocity I
1) it speeds up all the time
The graph of position versus
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down
5) not really sure
x
t
14 - Graphing Velocity I
1) it speeds up all the time
The graph of position versus
2) it slows down all the time
time for a car is given below.
3) it moves at constant velocity
What can you say about the
4) sometimes it speeds up and
velocity of the car over time?
sometimes it slows down
5) not really sure
x
The car moves at a constant velocity because
the x vs. t plot shows a straight line. The
slope of a straight line is constant. Remember
that the slope of x versus t is the velocity!
t
15 - Graphing Velocity II
The graph of position vs. time
1) it speeds up all the time
2) it slows down all the time
for a car is given below. What
3) it moves at constant velocity
can you say about the velocity
4) sometimes it speeds up and
of the car over time?
sometimes it slows down
5) not really sure
x
t
15 - Graphing Velocity II
1) it speeds up all the time
The graph of position vs. time
2) it slows down all the time
for a car is given below. What
3) it moves at constant velocity
can you say about the velocity
4) sometimes it speeds up and
of the car over time?
sometimes it slows down
5) not really sure
The car slows down all the time because the
x
slope of the x vs. t graph is diminishing as
time goes on. Remember that the slope of x
vs. t is the velocity! At large t, the value of the
position x does not change, indicating that the
car must be at rest.
t
16 - v versus t graphs I
1) decreases
Consider the line labeled A in the
2) increases
v versus t plot. How does the
3) stays constant
speed change with time for line
4) increases, then decreases
A?
5) decreases, then increases
v
A
t
B
16 - v versus t graphs I
1) decreases
Consider the line labeled A in the
2) increases
v versus t plot. How does the
3) stays constant
speed change with time for line
4) increases, then decreases
A?
5) decreases, then increases
v
A
In case A, the initial velocity is positive
t
B
and the magnitude of the velocity
continues to increase with time.
17 - v versus t graphs II
1) decreases
Consider the line labeled B in the
2) increases
v versus t plot. How does the
3) stays constant
speed change with time for line
4) increases, then decreases
B?
5) decreases, then increases
v
A
t
B
17 - v versus t graphs II
1) decreases
Consider the line labeled B in the
2) increases
v versus t plot. How does the
3) stays constant
speed change with time for line
4) increases, then decreases
B?
5) decreases, then increases
v
In case B, the initial velocity is positive
A
but the magnitude of the velocity
t
B
decreases toward zero. After this, the
magnitude increases again, but becomes
negative, indicating that the object has
changed direction.
18 - Rubber Balls I
v
v
1
3
t
v
2
You drop a rubber ball. Right after it
leaves your hand and before it hits
the floor, which of the above plots
represents the v vs. t graph for this
pointing up.)
t
t
4
v
t
18 - Rubber Balls I
v
v
1
3
t
v
2
You drop a rubber ball. Right after it
leaves your hand and before it hits
the floor, which of the above plots
represents the v vs. t graph for this
t
t
v
4
The ball is dropped from rest, so its initial
velocity is zero. Since the y-axis is pointing
upwards and the ball is falling downwards, its
velocity is negative and becomes more and
more negative as it accelerates downward.
pointing up.)
t
19 - Rubber Balls II
v
v
1
3
t
v
2
You toss a ball straight up in the air
and catch it again. Right after it
leaves your hand and before you
catch it, which of the above plots
represents the v vs. t graph for this
pointing up.)
t
v
4
t
t
19 - Rubber Balls II
v
v
1
3
t
v
2
You toss a ball straight up in the air
t
v
4
t
t
The ball has an initial velocity that is positive
and catch it again. Right after it
leaves your hand and before you
but diminishing as it slows. It stops at the top (v
catch it, which of the above plots
= 0), and then its velocity becomes negative and
represents the v vs. t graph for this
becomes more and more negative as it
pointing up.)
accelerates downward.
20 - Rubber Balls III
v
v
1
3
t
v
2
You drop a very bouncy rubber ball.
It falls, and then it hits the floor and
bounces right back up to you. Which
of the following represents the v vs.
t graph for this motion?
t
t
4
v
t
20 - Rubber Balls III
v
v
1
3
t
v
2
You drop a very bouncy rubber ball.
It falls, and then it hits the floor and
t
t
v
4
t
Initially, the ball is falling down, so its
velocity must be negative (if UP is positive).
Its velocity is also increasing in magnitude as
bounces right back up to you. Which
it falls. Once it bounces, it changes direction
of the following represents the v vs.
and then has a positive velocity, which is
t graph for this motion?
also decreasing as the ball moves upward.
21 - Rubber Balls IV
v
v
1
3
t
v
2
You drop a very bouncy rubber
ball. It falls, and then it hits the
floor and bounces right back up to
you. Which of the following
represents the v vs. t graph for this
motion?
t
t
4
v
t
21 - Rubber Balls IV
v
v
1
3
t
t
v
2
You drop a very bouncy rubber ball.
It falls, and then it hits the floor and
v
4
t
Initially, the ball is falling down, so its
velocity must be negative (if UP is positive).
Its velocity is also increasing in magnitude
bounces right back up to you.
t
as it falls. Once it bounces, it changes
Which of the following represents
direction and then has a positive velocity,
the v vs. t graph for this motion?
which is also decreasing as the ball moves
upward.
22 - Vectors I
1) same magnitude, but can be in any direction
If two vectors are given such 2) same magnitude, but must be in the same
that A + B = 0, what can you
direction
3) different magnitudes, but must be in the same
say about the magnitude and direction
direction of vectors A and
B?
4) same magnitude, but must be in opposite
directions
5) different magnitudes, but must be in opposite
directions
22 - Vectors I
If two vectors are given such
1) same magnitude, but can be in any direction
2) same magnitude, but must be in the same
that A + B = 0, what can you direction
say about the magnitude and 3) different magnitudes, but must be in the
direction of vectors A and
same direction
B?
4) same magnitude, but must be in opposite
directions
5) different magnitudes, but must be in
opposite directions
The magnitudes must be the same, but one vector must be pointing in the
opposite direction of the other, in order for the sum to come out to zero. You can
prove this with the tip-to-tail method.
23 - Vector Components I
If each component of a
1) it doubles
vector is doubled, what
2) it increases, but by less than double
happens to the angle of
3) it does not change
4) it is reduced by half
that vector?
5) it decreases, but not as much as half
23 - Vector Components I
If each component of a
1) it doubles
vector is doubled, what
2) it increases, but by less than double
happens to the angle of
3) it does not change
that vector?
4) it is reduced by half
5) it decreases, but not as much as half
The magnitude of the vector clearly doubles if each of its
components is doubled. But the angle of the vector is given by tan θ
= 2y/2x, which is the same as tan θ = y/x (the original angle).
Follow-up: If you double one component and not
the other, how would the angle change?
24 - Vector Components II
A certain vector has x and y components that
1) 30°
are equal in magnitude. Which of the following
2) 180°
is a possible angle for this vector, in a
3) 90°
standard x-y coordinate system?
4) 60°
5) 45°
24 - Vector Components II
A certain vector has x and y components
1) 30°
that are equal in magnitude. Which of the
2) 180°
following is a possible angle for this vector,
3) 90°
in a standard x-y coordinate system?
4) 60°
5) 45°
The angle of the vector is given by tan θ = y/x. Thus, tan θ = 1 in this
case if x and y are equal, which means that the angle must be 45°.
You are adding vectors of length 20
and 40 units. What is the only
1) 0
2) 18
possible resultant magnitude that
3) 37
you can obtain out of the following
4) 64
choices?
5) 100
You are adding vectors of length 20
and 40 units. What is the only
1) 0
2) 18
possible resultant magnitude that
3) 37
you can obtain out of the following
4) 64
choices?
5) 100
The minimum resultant occurs when the vectors are
opposite, giving 20 units. The maximum resultant occurs
when the vectors are aligned, giving 60 units. Anything in
between is also possible, for angles between 0° and 180°.
26 - Firing Balls I
A small cart is rolling at constant
1) it depends on how fast the cart is
velocity on a flat track. It fires a
moving
ball straight up into the air as it
2) it falls behind the cart
moves. After it is fired, what
3) it falls in front of the cart
happens to the ball?
4) it falls right back into the cart
5) it remains at rest
26 - Firing Balls I
A small cart is rolling at constant
1) it depends on how fast the cart is
velocity on a flat track. It fires a
moving
ball straight up into the air as it
2) it falls behind the cart
moves. After it is fired, what
3) it falls in front of the cart
happens to the ball?
4) it falls right back into the cart
5) it remains at rest
In the frame of reference of the
cart, the ball only has a vertical
component of velocity. So it goes
up and comes back down. To a
ground observer, both the cart
and the ball have the same
horizontal velocity, so the ball
still returns into the cart.
when
viewed from
train
when
viewed from
ground
27 - Firing Balls II
Now the cart is being pulled along 1) it depends upon how much the track
a horizontal track by an external
force (a weight hanging over the
table edge) and accelerating. It
fires a ball straight out of the
is tilted
2) it falls behind the cart
3) it falls in front of the cart
cannon as it moves. After it is
4) it falls right back into the cart
fired, what happens to the ball?
5) it remains at rest
27 - Firing Balls II
Now the cart is being pulled along a 1) it depends upon how much the track
horizontal track by an external force
is tilted
(a weight hanging over the table
edge) and accelerating. It fires a ball
2) it falls behind the cart
straight out of the cannon as it
3) it falls in front of the cart
moves. After it is fired, what
4) it falls right back into the cart
happens to the ball?
5) it remains at rest
Now the acceleration of the cart is completely unrelated to the ball. In fact, the
ball does not have any horizontal acceleration at all (just like the first question),
so it will lag behind the accelerating cart once it is shot out of the cannon.
28 - Dropping a Package
You drop a package from a
plane flying at constant
speed in a straight line.
Without air resistance, the
package will:
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
3) move ahead of the plane while
falling
4) not fall at all
28 - Dropping a Package
You drop a package from a
plane flying at constant
speed in a straight line.
Without air resistance, the
package will:
1) quickly lag behind the plane
while falling
2) remain vertically under the
plane while falling
3) move ahead of the plane while
falling
4) not fall at all
Both the plane and the package have the same
horizontal velocity at the moment of release.
They will maintain this velocity in the xdirection, so they stay aligned.
Follow-up: What would happen if air resistance is present?
29 - Dropping the Ball I
From the same height (and at
(1) the “dropped” ball
the same time), one ball is
(2) the “fired” ball
dropped and another ball is
(3) they both hit at the same time
fired horizontally. Which one
(4) it depends on how hard the ball
will hit the ground first?
was fired
(5) it depends on the initial height
29 - Dropping the Ball I
From the same height (and at
(1) the “dropped” ball
the same time), one ball is
(2) the “fired” ball
dropped and another ball is
(3) they both hit at the same time
fired horizontally. Which one
(4) it depends on how hard the ball
will hit the ground first?
was fired
(5) it depends on the initial height
Both of the balls are falling vertically under the influence of gravity. They
both fall from the same height. Therefore, they will hit the ground at the
same time. The fact that one is moving horizontally is irrelevant – remember
that the x and y motions are completely independent !!
Follow-up: Is that also true if there is air resistance?
30 - Dropping the Ball II
1) the “dropped” ball
In the previous problem,
2) the “fired” ball
which ball has the greater
3) neither – they both have the
velocity at ground level?
same velocity on impact
4) it depends on how hard the ball
was thrown
30 - Dropping the Ball II
1) the “dropped” ball
In the previous problem,
2) the “fired” ball
which ball has the greater
3) neither – they both have the
velocity at ground level?
same velocity on impact
4) it depends on how hard the ball
was thrown
Both balls have the same vertical velocity when
they hit the ground (since they are both acted on
by gravity for the same time). However, the “fired”
ball also has a horizontal velocity. When you add
the two components vectorially, the “fired” ball
has a larger net velocity when it hits the ground.
Follow-up: What would you have to do to have them
both reach the same final velocity at ground level?
31 - Dropping the Ball III
A projectile is launched from
1) just after it is launched
the ground at an angle of 30o.
2) at the highest point in its flight
At what point in its trajectory
3) just before it hits the ground
does this projectile have the
4) halfway between the ground and the
least speed?
highest point
5) speed is always constant
31 - Dropping the Ball III
A projectile is launched from the
1) just after it is launched
ground at an angle of 30o. At
2) at the highest point in its flight
what point in its trajectory does
3) just before it hits the ground
this projectile have the least
speed?
4) halfway between the ground and the
highest point
5) speed is always constant
The speed is smallest at the
highest point of its flight path
because the y-component of
the velocity is zero.
32 - Punts I
Which of the 3
punts has the
h
longest hang
time?
1
2
4) all have the same hang time
3
32 - Punts I
Which of the 3
punts has the
h
longest hang
1
time?
2
4) all have the same hang time
The time in the air is determined by the vertical motion ! Since
all of the punts reach the same height, they all stay in the air
for the same time.
Follow-up: Which one had the greater initial velocity?
3
33 - Punts II
A battleship simultaneously fires two shells at two enemy
submarines. The shells are launched with the same initial velocity.
If the shells follow the trajectories shown, which submarine gets
hit first ?
1
2
3) both at the same time
33 - Punts II
A battleship simultaneously fires two shells at two enemy
submarines. The shells are launched with the same initial velocity.
If the shells follow the trajectories shown, which submarine gets
hit first ?
The flight time is fixed by the motion
in the y-direction. The higher an
object goes, the longer it stays in
flight. The shell hitting ship #2 goes
less high, therefore it stays in flight
1
for less time than the other shell.
Thus, ship #2 is hit first.
2
3) both at the same time
Follow-up: Which one traveled the greater distance?
34 - Cannon on the Moon
For a cannon on Earth, the cannonball would follow path 2.
Instead, if the same cannon were on the Moon, where g = 1.6
m/s2, which path would the cannonball take in the same
situation?
1
2
3
4
34 - Cannon on the Moon
For a cannon on Earth, the cannonball would follow path 2.
Instead, if the same cannon were on the Moon, where g = 1.6
m/s2, which path would the cannonball take in the same
situation?
The ball will spend more
time in the air because gMoon
< gEarth. With more time, it
1
2
can travel farther in the
horizontal direction.
Follow-up: Which path would it take in outer space?
3
4
1) 15°
projectiles at different angles with the same
2) 30°
launch speed. At what angle should the
3) 45°
projectile be launched in order to travel the
4) 60°
greatest distance before landing?
5) 75°
1) 15°
projectiles at different angles with the same
2) 30°
launch speed. At what angle should the
3) 45°
projectile be launched in order to travel the
4) 60°
greatest distance before landing?
5) 75°
A steeper angle lets the projectile stay in the air longer, but it does not
travel so far because it has a small x-component of velocity. On the other
hand, a shallow angle gives a large x-velocity, but the projectile is not in
the air for very long. The compromise comes at 45°, although this result is
best seen in a calculation of the “range formula” as shown in the
textbook.
36 - Shoot the Monkey I
You are trying to hit a friend with a
1) yes, it hits
water balloon. He is sitting in the
2) maybe – it depends on
window of his dorm room directly
across the street. You aim straight at
him and shoot. Just when you shoot,
he falls out of the window! Does the
the speed of the shot
3) no, it misses
4) the shot is impossible
5) not really sure
water balloon hit him?
Assume that the shot does have
enough speed to reach the dorm
36 - Shoot the Monkey I
You are trying to hit a friend with a
1) yes, it hits
water balloon. He is sitting in the
2) maybe – it depends on
window of his dorm room directly
across the street. You aim straight at
him and shoot. Just when you shoot,
he falls out of the window! Does the
Yourwater
friend
falls under
the
balloon
hit him?
influence of gravity, just like the
water balloon. Thus, they are both
undergoing free fall in the ydirection. Since the slingshot was
accurately aimed at the right
height, the water balloon will fall
exactly as your friend does, and it
the speed of the shot
3) no, it misses
4) the shot is impossible
5) not really sure
Assume that the shot does have
enough speed to reach the dorm
37 - Shoot the Monkey II
You’re on the street, trying to hit a
1) yes, it hits
friend with a water balloon. He sits in
2) maybe – it depends on
his dorm room window above your
the speed of the shot
position. You aim straight at him and
3) the shot is impossible
shoot. Just when you shoot, he falls
4) no, it misses
out of the window! Does the water
5) not really sure
balloon hit him??
Assume that the shot does
have enough speed to reach
37 - Shoot the Monkey II
You’re on the street, trying to hit a
1) yes, it hits
friend with a water balloon. He sits in
2) maybe – it depends on
his dorm room window above your
the speed of the shot
position. You aim straight at him and
3) the shot is impossible
shoot. Just when you shoot, he falls
4) no, it misses
out of the window! Does the water
5) not really sure
balloon hit him??
This is really the same situation as
before!! The only change is that
the initial velocity of the water
balloon now has a y-component
as well. But both your friend and
the water balloon still fall with the
same acceleration -- g !!
Assume that the shot does
have enough speed to reach
38 - Shoot the Monkey III
You’re on the street, trying to hit a friend
1) yes, they hit
with a water balloon. He sits in his dorm
2) maybe – it depends on the
room window above your position and is
speeds of the shots
aiming at you with HIS water balloon!
3) the shots are impossible
You aim straight at him and shoot and he
4) no, they miss
does the same in the same instant. Do
5) not really sure
the water balloons hit each other?
38 - Shoot the Monkey III
You’re on the street, trying to hit a friend
1) yes, they hit
with a water balloon. He sits in his dorm
2) maybe – it depends on the
room window above your position and is
speeds of the shots
3) the shots are impossible
aiming at you with HIS water balloon!
You aim straight at him and shoot and he
4) no, they miss
5) not really sure
does the same in the same instant. Do
the water balloons hit each other?
This is still the same situation!!
Both water balloons are aimed
straight at each other and both
still fall with the same acceleration
-- g !!
Follow-up: When would they NOT hit each other?
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