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PY1P10 - Physics of Motion - Assignment #1
Due: 11:00pm on Tuesday, October 26, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
Welcome to your first Physics tutorial assignment based on your lecture material.
Please remember that you should record all your attempts and rough work for each question in a hardback notebook. This will allow you to effectively
review and revise the material covered in this assignment at a later date.
Running and Walking
Description: One person walks half of a distance and runs the other half. Another person covers the same distance by running and walking
for the same amount of time. Determine total time taken by each, and their average velocities.
Tim and Rick both can run at speed
and walk at speed
, with
. They set off together on a journey of distance
. Rick walks half of
the distance and runs the other half. Tim walks half of the time and runs the other half.
Part A
How long does it take Rick to cover the distance
Hint A.1
?
Compute midpoint for Rick
Find the time that it takes Rick to walk the first half of the distance, that is, to travel a distance
at speed
.
ANSWER:
=
Hint A.2
Compute running time for Rick
Now find the time Rick spends running.
ANSWER:
=
Hint A.3
What equation to use
Now just add the two times up and you're done.
Express the time taken by Rick in terms of
,
, and
.
ANSWER:
=
Part B
Find Rick's average speed for covering the distance
Hint B.1
Calculate velocity using
.
and time
You were given the total distance and have calculated the total time. Recall that average velocity is equal to total distance traveled divided
by the amount of time it took to travel this distance.
Express Rick's average speed in terms of
and
.
ANSWER:
=
Part C
How long does it take Tim to cover the distance?
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Hint C.1
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Calculate average speed
Tim walks at speed
Hint C.1.1
half the time and runs at speed
for the other half.
Solve a related problem
Consider a related problem. Tim walks for a time
Find the total distance he travels in time
at speed
and runs for a time
in terms of given quantities and
at speed
.
.
ANSWER:
=
Now use this expression for
to find Tim's average speed.
Find Tim's average speed in terms of given quantities.
ANSWER:
=
From this result, you can see that when a journey consists of equal amounts of time walking and running, the average speed will be
equal to the simple average of the walking and running speeds. This is not the case when the journey is broken into walking and
running segments in some other manner.
Express the time taken by Tim in terms of
,
, and
.
ANSWER:
=
Part D
Who covers the distance
Hint D.1
more quickly?
Consider the relative positions at the midpoint
Imagine that both Rick and Tim do all of their walking before they start to run. Rick will start running when he has covered half of the total
distance. When Tim reaches half of the total distance, will he already have started running?
Think logically, but without using the detailed answers in the previous parts.
ANSWER:
Rick
Tim
Neither. They cover the distance in the same amount of time.
Part E
In terms of given quantities, by what amount of time,
, does Tim beat Rick?
It will help you check your answer if you simplify it algebraically and check the special case
Express the difference in time,
in terms of
,
, and
.
.
ANSWER:
=
Part F
In the special case that
Hint F.1
If
, what would be Tim's margin of victory
?
Think it through
, is the any difference between what Tim and Rick do?
ANSWER:
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Page 3 of 4
Speed of a Bullet
Description: This problem reviews speed from the angle between bullet holes in two disks following a standard experiment.
A bullet is shot through two cardboard disks attached a distance
apart to a shaft turning with a rotational period
, as shown.
Part A
Derive a formula for the bullet speed
the hole in the second. If required, use
in terms of
,
, and a measured angle
between the position of the hole in the first disk and that of
, not its numeric equivalent. Both of the holes lie at the same radial distance from the shaft.
means that the holes are in a line and
measures the angular displacement between the two holes; for instance,
means that
when one hole is up, the other is down. Assume that the bullet must travel through the set of disks within a single revolution.
Hint A.1
Consider hole positions
The relative position of the holes can be used to find the bullet's speed. Remember, the shaft will have rotated while the bullet travels
between the disks.
Hint A.2
How long does it take for the disks to rotate by an angle ?
The disks rotate by 2
Hint A.2.1
in time
. How long will it take them to rotate by ?
Checking your formula
If your formula is correct, when you plug 2
Give your answer in terms of
in for , your answer will be
, , and constants such as
.
.
ANSWER:
=
You know that the bullet went a distance
in the time it took for the disks to rotate by .
ANSWER:
=
Exercise 2.34
Description: A subway train starts from rest at a station and accelerates at a rate of 1.60 m/s^2 for 14.0 s . It runs at constant speed for 70.0 s
and slows down at a rate of 3.50 m/s^2 until it stops at the next station. (a) Find the total distance covered.
A subway train starts from rest at a station and accelerates at a rate of
for 14.0
. It runs at constant speed for 70.0
and slows
until it stops at the next station.
down at a rate of
Part A
Find the total distance covered.
ANSWER:
=
Exercise 2.50
Description: The acceleration of a bus is given by a_x(t)= alpha t, where alpha is a constant. (a) If the bus's velocity at time t_1 is v_1, what is
its velocity at time t_2? (b) If the bus's position at time t_1 is x_1, what is its position at time t_2?
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The acceleration of a bus is given by
, where
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= 1.28
is a constant.
Part A
If the bus's velocity at time
= 1.00
is 4.90
= 1.00
is 6.00
, what is its velocity at time
= 2.11 ?
ANSWER:
=
Part B
If the bus's position at time
, what is its position at time
= 2.11 ?
ANSWER:
=
Problem 2.97
Description: A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of t later. You
may ignore air resistance. (a) If the height of the building is h, what must the initial speed be of the first ball if ...
A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof a time of 1.20
air resistance.
later. You may ignore
Part A
If the height of the building is 19.8
, what must the initial speed be of the first ball if both are to hit the ground at the same time?
ANSWER:
=
Part B
Consider the same situation, but now let the initial speed
of the first ball be given and treat the height
What must the height of the building be for both balls to reach the ground at the same time for
= 8.70
of the building as an unknown.
.
ANSWER:
=
Part C
If
is greater than some value
, a value of
does not exist that allows both balls to hit the ground at the same time. Solve for
.
ANSWER:
=
Part D
If
is less than some value
, a value of
does not exist that allows both balls to hit the ground at the same time. Solve for
.
ANSWER:
=
Score Summary:
Your score on this assignment is 0%.
You received 0 out of a possible total of 100 points.
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