Between Sept 25 and Sept 27
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University of Windsor *
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Course
1400
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
7
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Between Sept 25 and Sept 27
Due: 11:59pm on Wednesday, September 27, 2023
You will receive no credit for items you complete after the assignment is due.
Grading Policy
Question 2.12
As a freely falling object speeds up, what is happening to its acceleration - does it increase, decrease, or stay the same?
Part A
Ignore air resistance.
ANSWER:
Correct
Part B
Consider air resistance.
ANSWER:
Correct
Tossing Balls off a Cliff
Learning Goal:
To clarify the distinction between speed and velocity, and to review qualitatively one-dimensional kinematics.
A woman stands at the edge of a cliff, holding one ball in each hand. At time
, she throws one ball straight up with speed
and the other straight down, also with speed
.
increases
decreases
stays the same
increases
decreases
stays the same
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For the following questions neglect air resistance. Pay particular attention to whether the answer involves "absolute" quantities
that have only magnitude (e.g., speed) or quantities that can have either sign (e.g., velocity). Take upward to be the positive
direction.
Part A
If the ball that is thrown downward has an acceleration of magnitude
at the instant of its release (i.e., when there is no
longer any force on the ball due to the woman's hand), what is the relationship between
and
, the magnitude of the
acceleration of gravity?
ANSWER:
Correct
Part B
Which ball has the greater acceleration at the instant of release?
ANSWER:
Correct
Part C
Which ball has the greater speed at the instant of release?
Hint 1.
Consider the initial speeds
Both of the balls were given initial speed
.
ANSWER:
the ball thrown upward
the ball thrown downward
Neither; the accelerations of both balls are the same.
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Correct
Part D
Which ball has the greater average speed during the 1-s interval after release (assuming neither hits the ground during that
time)?
Hint 1.
How to approach the problem
This question asks which ball has the greater average speed during the first second after release. You already know
that the speed of the two balls is the same at the instant of release. However, the ball thrown downward starts to
speed up due to gravity, whereas the ball thrown upward starts to slow down. So the instantaneous speed after the
first second of flight is different for the two balls.
ANSWER:
Correct
Part E
Which ball hits the ground with greater speed?
ANSWER:
Correct
A Flea in Flight
the ball thrown upward
the ball thrown downward
Neither; the speeds are the same.
the ball thrown upward
the ball thrown downward
Neither; the average speeds of both balls are the same.
the ball thrown upward
the ball thrown downward
Neither; the balls hit the ground with the same speed.
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In this problem, you will apply kinematic equations to a jumping flea. Take the magnitude of free-fall acceleration to be 9.80
. Ignore air resistance.
Part A
A flea jumps straight up to a maximum height of 0.490
. What is its initial velocity
as it leaves the ground?
Express your answer in meters per second to three significant figures.
Hint 1.
Finding the knowns and unknowns
Take the positive
y
direction to be upward, the
y
coordinate of the initial position of the flea to be
, and denote
the final height of the flea by
, whose value 0.490
you know. Let
be the duration of the flea's leap to its
maximum height,
its initial velocity,
its final velocity (at maximum height), and
its (constant) acceleration.
Which of the following quantities is/are known?
Check all that apply.
Hint 1.
The number of known quantities
Typically, you need to know the values of four variables in order to solve any of the kinematic equations,
because they contain five variables each, with the exception of
, which contains only four
variables, in which case you would need to know the values of only three of these variables. Since we may
place the flea at any point of the
y
axis to begin its jump, we have conveniently assumed that
is equal to 0.
Hint 2.
What is the flea's velocity at its maximum height?
What is the velocity
of the flea at its maximum height of
0.490
?
Express your answer in meters per second to three significant figures.
ANSWER:
ANSWER:
Hint 2.
Determine which kinematic equation to use
Decide which kinematic equation makes the solution of this problem easiest. That is, look for an equation that
contains the variable you are solving for and in which all the other variables are known.
ANSWER:
= 0
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Hint 3.
Some algebra help
You have determined that the simplest equation to use is
.
To solve for
, you must first subtract the term
from both sides of the equation, and then take the
square root of both sides. Keep in mind that the acceleration is negative.
ANSWER:
Correct
Part B
How long is the flea in the air from the time it jumps to the time it hits the ground?
Express your answer in seconds to three significant figures.
Hint 1.
How to approach the problem
One approach is to find the time it takes for the flea to go from the ground to its maximum height, and then find the
time it takes for the flea to fall from its maximum height to the ground. The subsequent hints will guide you through
this approach.
Hint 2.
Find the time from the ground to the flea's maximum height
What is the time
it takes the flea to go from the ground (
,
) to its maximum height (
0.490
,
)?
Express your answer in seconds to three significant figures.
ANSWER:
Hint 3.
Find the time from the flea's maximum height to the ground
What is the time
that it takes for the flea to fall from its maximum height (
0.490
,
) to the
ground (
)?
Express your answer in seconds to three significant figures.
= 3.10
= 0.316
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ANSWER:
ANSWER:
Correct
Notice that the time for the flea to rise to its maximum height is equal to the time it takes for it to fall from that
height back to the ground. This is a general feature of projectile motion (any motion with
) when air
resistance is neglected and the landing point is at the same height as the launch point.
There is also a way to find the total time in the air in one step: just use
and realize that you are looking for the value of
for which
.
Question 2.11
A baseball player hits a ball straight up into the air. It leaves the bat with a speed of 150
. Ignore air resistance.
Part A
How fast would the ball be traveling when the catcher catches it (at the same height it left the bat)?
Express your answer in kilometers per hour.
ANSWER:
Correct
Anderson Video - Time for Dropped Object to Hit Ground
First, launch the video
Time for Dropped Object to Hit the Ground
. After watching the video, answer the follow-up question below.
= 0.316
time in air =
0.632
= 150
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Part A
A tourist drops (from rest) a ping pong ball from the top of the tower, which has a height of 474 meters. Assuming no air
resistance, how long does it take for the ping pong ball to hit the ground?
Express your answer to three significant figures and include the appropriate units.
ANSWER:
Correct
Score Summary:
Your score on this assignment is 100%.
You received 5 out of a possible total of 5 points.
= 9.84