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PY1P10 - Physics of Motion - Assignment #1
Due: 11:00pm on Monday, October 24, 2011
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
journey of distance
and walk at speed
, with
. They set off together on a
. 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
?
Compute midpoint for Rick
Hint A.1
Find the time that it takes Rick to walk the first half of the distance, that is, to travel a distance
speed
at
.
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.
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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?
Hint C.1
Calculate average speed
Tim walks at speed
half the time and runs at speed
for the other half.
Hint C.1.1 Solve a related problem
Consider a related problem. Tim walks for a time
speed
at speed
and runs for a time
at
.
Find the total distance he travels in time
in terms of given quantities and
.
ANSWER:
=
Now use this expression for
to find Tim's average speed.
Find Tim's average speed in terms of given quantities.
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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
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In the special case that
Hint F.1
, what would be Tim's margin of victory
?
Think it through
, is the any difference between what Tim and Rick do?
If
ANSWER:
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
period
apart to a shaft turning with a rotational
, as shown.
Part A
Derive a formula for the bullet speed
in terms of
,
, and a measured angle
of the hole in the first disk and that of the hole in the second. If required, use
equivalent. Both of the holes lie at the same radial distance from the shaft.
displacement between the two holes; for instance,
between the position
, not its numeric
measures the angular
means that the holes are in a line and
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
in time
. How long will it take them to rotate by ?
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Hint A.2.1 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.
for 14.0
A subway train starts from rest at a station and accelerates at a rate of
constant speed for 70.0
and slows down at a rate of
. It runs at
until it stops at the next station.
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?
, where
The acceleration of a bus is given by
= 1.14
is a constant.
Part A
If the bus's velocity at time
= 1.20
is 4.96
, what is its velocity at time
= 2.15 ?
ANSWER:
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=
Part B
If the bus's position at time
= 1.20
is 6.08
, what is its position at time
= 2.15 ?
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 1.07 later. You may ignore air resistance.
Part A
If the height of the building is 20.6
, 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
of the building as an unknown. What must the height of the building be for both balls to reach the
ground at the same time for
= 9.00
.
ANSWER:
=
Part C
If
is greater than some value
at the same time. Solve for
, a value of
does not exist that allows both balls to hit the ground
.
ANSWER:
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=
Part D
If
is less than some value
the same time. Solve for
, a value of
does not exist that allows both balls to hit the ground at
.
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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