Problem 2A - Hays High School

NAME ______________________________________ DATE _______________ CLASS ____________________
Holt Physics
Problem 2A
AVERAGE VELOCITY AND DISPLACEMENT
PROBLEM
The fastest fish, the sailfish, can swim 1.2 × 10 2 km/h. Suppose you have
a friend who lives on an island 16 km away from the shore. If you send
a message using a sailfish as a messenger, how long will it take for the
message to reach your friend
SOLUTION
Given: v avg = 1.2 × 10 2 km/h
∆x = 16 km
Unknown: ∆t =
Use the definition of average speed to find ∆t.
v avg = ⎯ ∆ ⎯
x
∆t
Rearrange the equation to calculate ∆t.
∆x
∆t = ⎯⎯
v avg
16 km
∆t = ⎯⎯⎯ =
1.2 × 10 2 ⎯ k m
h
⎯
1 h
⎯⎯ 60 min
= 8.0 min
16
km
⎯⎯
2.0 km/
min
HRW material copyrighted under notice appearing earlier in this book.
ADDITIONAL PRACTICE
1. The Sears Tower in Chicago is 443 m tall. Joe wants to set the world’s
stair climbing record and runs all the way to the roof of the tower. If Joe’s
average upward speed is 0.60 m/s, how long will it take Joe to climb from
street level to the roof of the Sears Tower
2. An ostrich can run at speeds of up to 72 km/h. How long will it take an
ostrich to run 1.5 km at this top speed
3. A cheetah is known to be the fastest mammal on Earth, at least for short
runs. Cheetahs have been observed running a distance of 5.50 × 10 2 m
with an average speed of 1.00 × 10 2 km/h.
a. How long would it take a cheetah to cover this distance at this speed
b. Suppose the average speed of the cheetah were just 85.0 km/h.
What distance would the cheetah cover during the same time interval
calculated in (a)
Problem 2A 3

NAME ______________________________________ DATE _______________ CLASS ____________________
4. A pronghorn antelope has been observed to run with a top speed of
97 km/h. Suppose an antelope runs 1.5 km with an average speed of
85 km/h, and then runs 0.80 km with an average speed of 67 km/h.
a. How long will it take the antelope to run the entire 2.3 km
b. What is the antelope’s average speed during this time
5. Jupiter, the largest planet in the solar system, has an equatorial radius of
about 7.1 × 10 4 km (more than 10 times that of Earth). Its period of rotation,
however, is only 9 h, 50 min. That means that every point on
Jupiter’s equator “goes around the planet” in that interval of time. Calculate
the average speed (in m/s) of an equatorial point during one period
of Jupiter’s rotation. Is the average velocity different from the average
speed in this case
6. The peregrine falcon is the fastest of flying birds (and, as a matter of fact,
is the fastest living creature). A falcon can fly 1.73 km downward in 25 s.
What is the average velocity of a peregrine falcon
7. The black mamba is one of the world’s most poisonous snakes, and with
a maximum speed of 18.0 km/h, it is also the fastest. Suppose a mamba
waiting in a hide-out sees prey and begins slithering toward it with a
velocity of +18.0 km/h. After 2.50 s, the mamba realizes that its prey can
move faster than it can. The snake then turns around and slowly returns
to its hide-out in 12.0 s. Calculate
a. the mamba’s average velocity during its return to the hideout.
b. the mamba’s average velocity for the complete trip.
c. the mamba’s average speed for the complete trip.
8. In the Netherlands, there is an annual ice-skating race called the “Tour of
the Eleven Towns.” The total distance of the course is 2.00 × 10 2 km, and
the record time for covering it is 5 h, 40 min, 37 s.
a. Calculate the average speed of the record race.
b. If the first half of the distance is covered by a skater moving with
a speed of 1.05v, where v is the average speed found in (a), how
long will it take to skate the first half Express your answer in hours
and minutes.
HRW material copyrighted under notice appearing earlier in this book.
4
Holt Physics Problem Workbook

Motion In One Dimension
Chapter 2
Additional Practice 2A
Givens
Solutions
1. ∆x = 443 m
v avg = 0.60 m/s
∆x
443
m
∆t = ⎯⎯ = ⎯⎯ = 740 s = 12 min, 20 s
v avg
0 .60
m/s
2. v avg = 72 km/h
∆x = 1.5 km
∆x
1.5 km
∆t = ⎯⎯ = ⎯⎯ = 75 s
v avg
72 ⎯k m ⎯
h ⎯ 1 h
⎯ 3600s
3. ∆x = 5.50 × 10 2 m
v avg = 1.00 × 10 2 km/h
∆x
5.50 × 10 2 m
a. ∆t = ⎯⎯ = ⎯⎯⎯⎯ =
v
avg
1.00 × 10 2 ⎯ k m
h
⎯
1 h
⎯⎯ 36 00s
⎯ 1 000
m
⎯
1 km
19.8 s
II
v avg = 85.0 km/h
b. ∆x =∆v avg ∆t
1 h
∆x = (85.0 km/h)
⎯⎯ 36 00s
⎯ 1 3
0 m
⎯
1 km
(19.8 s) = 468 m
Copyright © by Holt, Rinehart and Winston. All rights reserved.
4. ∆x 1 = 1.5 km
v 1 = 85 km/h
∆x 1 = 0.80 km
v 2 = 67 km/h
5. r = 7.1 × 10 4 km
∆t = 9 h, 50 min
a. ∆t tot =∆t 1 +∆t 2 = ⎯ ∆ x1
⎯ + ⎯ ∆ x2
⎯
v1
v2
1.5 km
0.80 km
∆t tot = ⎯⎯ + ⎯⎯ =64 s + 43 s = 107 s
67 ⎯k m ⎯
h ⎯ 1 h
⎯
85 ⎯k m ⎯
h ⎯ 1 h
⎯ 3600s
3600s
∆x 1.5 km + 0.80 km 2.3 km
b. v avg = 1 +∆x
⎯ 2
= ⎯⎯ = ⎯⎯ = 77 km/h
∆t1 +∆t 2 (64 s + 43 s) 1 h
(107 s) 1 h
⎯36
⎯
⎯3
⎯ 600
00s
∆x = 2πr
∆x 2π(7.1 × 10 7 m)
4.5 × 10 8 m
v avg = ⎯ = ⎯⎯⎯⎯ = ⎯⎯⎯
∆t
60
s
(540 min + 50 min) ⎯ ⎯
(9 h) ⎯60 min
⎯
1 h
+ 50 min ⎯ 60
s
⎯ 1 min
1 min
4.5 × 10 8 m
v avg = ⎯⎯
60
s
(590 min) ⎯ ⎯ 1 min
v avg = 1.3 × 10 4 m/s
Thus the average speed = 1.3 × 10 4 m/s.
On the other hand, the average velocity for this point is zero, because the point’s displacement
is zero.
Section Two — Problem Workbook Solutions II Ch. 2–1

Givens
6. ∆x = –1.73 km
∆t = 25 s
Solutions
∆x
v avg = =⎯ –1.73 × 10 3 m
⎯ ⎯ = –69 m/s = –250 km/h
∆t 25
s
7. v avg,1 = 18.0 km/h
∆t 1 = 2.50 s
∆t 2 = 12.0 s
1 h
a. ∆x 1 = v avg,1 ∆t 1 = (18.0 km/h)
⎯⎯ 36 00s
⎯ 1 3
0 m
⎯
1 km
(2.50s) = 12.5 m
∆x 2 = –∆x 1 = –12.5 m
v avg,2 = ⎯ ∆ x
⎯ 2 = ⎯ – 12.
5 m
⎯ =
∆t 2 12.
0 s
–1.04 m/s
b. v avg,tot = ⎯ ∆ x1
+ ∆x2
⎯ = ⎯ 12. 5 m + (−12.5
m) 0.0 m
⎯ = ⎯ =
∆t1
+ ∆t 2 2.50
s + 12.0
s 14.5 s
0.0 m/s
II
c. total distance traveled =∆x 1 – ∆x 2 = 12.5 m – (–12.5 m) = 25.0 m
total time of travel =∆t 1 +∆t 2 = 2.50 s + 12.0 s = 14.5 s
average speed = ⎯ to tal
distance
⎯ = ⎯ 2 5.
0 m
⎯ = 1.72 m/s
total
time
14.
5 s
8. ∆x = 2.00 × 10 2 km
∆t = 5 h, 40 min, 37 s
a. v avg = ⎯ ∆ x
2.00 × 10 5 m
⎯ = =⎯ 2.0 0 × 10 5 ⎯⎯⎯⎯⎯ ⎯
∆t
0s
s
20
437
sm
5 h ⎯360 60
⎯
h
+
40 min
⎯ ⎯ m in
+ 37 s
v avg =
9.79 m/s = 35.2 km/h
v avg = (1.05)v avg
∆x = ⎯ 1 2 ⎯ ∆x
⎯2.00 × 10 5 m
⎯ 2
∆x
b. ∆t = ⎯ = ⎯⎯ =9.73 × 10 3 s
vavg
(1.05)
9.79 ⎯ m s ⎯
∆t = (9.73 × 10 3 1 h
s)
⎯⎯ 36 00s
= 2.70 h
(0.70 h)
⎯ 60 min
⎯
1h
= 42 min
∆t = 2 h, 42 min
Copyright © by Holt, Rinehart and Winston. All rights reserved.
II Ch. 2–2
Holt Physics Solution Manual