Gibilisco S. Everyday Math Demystified: A Self-Teaching Guide

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Thus, the change in momentum is p

 p

¼ 30ó000 kg  m=s  40ó000 kg  m=s ¼10ó000 kg  m=s

in a northerly direction

That is the same as 10,000 kg  m/s in a southerly direction. Because impulse

is the same thing as the change in momentum, the impulse is 10,000 kg  m/s

in a southerly direction.

Don’t let this result confuse you. A vector with a magnitude of x in a

certain direction is, in the real world, a vector with magnitude þx in the exact

opposite direction. Problems sometimes work out to yield vectors with

negative magnitude. When that happens, reverse the direction and change

the sign of the magnitude from minus to plus.

Quiz

Refer to the text in this chapter if necessary. A good score is eight correct.

Answers are in the back of the book.

1. If you drive a 1000-kg vehicle down the road at 30 m/s, what is the

momentum?

(a) 33 kg  m/s

(b) 1030 kg  m/s

(d) 30,000 kg  m/s

2. Why is it unwise to drive a pickup truck full of loose bricks?

(a) If you suddenly have to swerve, the bricks’ momentum could

cause some of them to suddenly ﬂy over the side onto the road

or into the ditch.

(b) If you suddenly have to stop, the bricks’ momentum could cause

some of them to sail through the back window and hit you.

tum could cause some of them to be dumped oﬀ the back of the

truck and onto the road.

(d) All of the above.

3. If you drive a truck full of loose bricks down a straight, level stretch of

highway, the momentum vector of each brick points

(a) in the same direction as the truck travels

(b) in the opposite direction from that in which the truck travels

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(d) nowhere, because momentum is not a vector

4. Imagine that a boat whose mass is 500 kg (with you and all your gear

in it) is traveling straight forward on a lake at 10 m/s. You cut the

engine and lift it out of the water, so you are coasting straight forward

at 10 m/s. What impulse vector will bring the boat to a stop? Assume

the boat moves along the water with no friction, and that there is no

wind or current.

(a) 50 kg  m/s, pointing forward.

(b) 50 kg  m/s, pointing backward.

(d) 5000 kg  m/s, pointing backward.

5. Suppose the town of Blissville is 5400 km from the town of Happyton,

as measured along the Interstate highways. You drive from Blissville

to Happyton over the course of several days, and you keep track of

your total driving time. You come to the conclusion that you were

traveling at an average speed of 15 m/s. How many hours were you

driving?

(a) 19

(b) 100

(d) It is impossible to answer this without more information.

6. Imagine the space-ship scenario described in the text and illustrated in

Fig. 15-10. Suppose a rocket engine is to be installed in a position and

orientation such that, when it is ﬁred, it causes the ship to slow down

but continue in the same direction. Where should such a rocket be

placed, and in what direction should its exhaust come out?

(a) It should be placed on the nose of the ship, and its exhaust should

come out directly forward.

(b) It should be placed on the nose of the ship, and its exhaust should

come out directly backward.

should come out directly sideways.

(d) Any of the above.

7. Suppose you buy a car and the manufacturer claims that it can accel-

erate from 0 to 30 m/s in 6 seconds. Suppose you take the car for a test

drive on a straight, level, dry stretch of roadway on a racetrack (with

the permission of the track owner and under the supervision of the

highway patrol, of course!). You discover that the manufacturer’s

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claim is true. What is the average acceleration rate during the

6-second period during which your car’s speed has increased from

a dead stop to 30 m/s?

(a) 5 m/s

(b) 30 m/s

(d) It is impossible to answer this without more information.

8. Suppose you have a mass of 60 kg on the earth’s surface. The moon

has a gravitational ﬁeld that is 1/6 as strong, at the surface, as the

earth’s gravitational ﬁeld. If you travel to the moon, what will be

your mass there?

(a) 10 kg

(b) 60 kg

(d) It is impossible to know without more information.

9. If you stand on the surface of the earth, your mass vector points

(a) straight down

(b) straight up

(d) nowhere, because mass is not a vector

10. Suppose you get a new set of tires for your truck, and they are

larger in diameter than the tires you have been using. You know

that your odometer was accurate with your old tires. If you drive

100 km with the new tires, your odometer, which measures distance

according to the number of axle rotations, will tell you that you

have traveled

(a) less than 100 km

(b) exactly 100 km

(d) too fast

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Test: Part 4

Do not refer to the text when taking this test. You may draw diagrams or use

a calculator if necessary. A good score is at least 30 correct. Answers are in

the back of the book. It’s best to have a friend check your score the ﬁrst time,

so you won’t memorize the answers if you want to take the test again.

1. Which of the following represents an arithmetic sequence?

(a) 0, 1, 2, 4, 8, 16, 32

(b) 2, 5, 8, 11, 14, 17, 20

(d) 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7

(e) 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64

2. A car is advertised as being capable of going from 0 to 60 miles per

hour in 5 seconds. What is the average acceleration, in miles per

hour per second (mi/hr/s) that this ﬁgure represents?

(a) 5 mi/hr/s

(b) 10 mi/hr/s

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(d) 300 mi/hr/s

(e) More information is necessary to calculate it.

3. Suppose that when you ‘‘ﬂoor’’ the gas pedal in your car, it produces

a certain constant forward force. This results in a certain forward

acceleration when you’re all alone in the car. If you ﬁll up the car

with passengers so its mass increases by 25% compared to its mass

when you are alone in it, and then you ‘‘ﬂoor’’ the gas pedal, what

happens to the forward acceleration? Ignore any possible eﬀects of

friction. Remember that force is the product of mass and acceleration.

(a) The acceleration becomes 1.25 times as great as it is with only you

in the car.

(b) The acceleration stays the same as it is with only you in the car.

you in the car.

(d) The acceleration becomes 3/4 as great as it is with only you

in the car.

(e) The acceleration becomes half as great as it is with only you in

the car.

4. Suppose that when you ‘‘ﬂoor’’ the gas pedal in your car, it produces

a certain constant forward force. This results in a certain forward

acceleration when you’re all alone in the car. If you put high-

performance fuel in the tank, producing a 25% increase in the force

produced when you ‘‘ﬂoor’’ the gas pedal, what happens to the

forward acceleration when you are alone in the car and you ‘‘ﬂoor’’

the gas pedal? Ignore any possible eﬀects of friction. Remember

that force is the product of mass and acceleration.

(a) The acceleration stays the same as it is with the ordinary fuel.

(b) The acceleration becomes 1.25 times as great as it is with the

ordinary fuel.

(d) The acceleration becomes twice as great as it is with the ordinary

fuel.

(e) The acceleration becomes four times as great as it is with the

ordinary fuel.

5. A quantity that has magnitude and direction is known as

(a) a variable

(b) a constant

Test: Part 4 385

(d) a vector

(e) a logarithm

6. Imagine that you’ve purchased a new hi-ﬁ audio ampliﬁer for

your car. It contains volume (or gain) control knobs, one for each

channel, calibrated in numbers from 0 to 10. The speciﬁcation

sheet in the instruction manual for your new ampliﬁer contains a

graph that looks like Fig. Test 4-1. From this graph, it is apparent that

(a) the output volume, in watts, is directly proportional to the volume

control setting in either channel

(b) the output volume, in decibels, is directly proportional to the

volume control setting in either channel

(d) the output volume, in decibels, is inversely proportional to the

volume control setting in either channel

(e) the output volume increases according to the square of the volume

control setting in either channel

Fig. Test 4-1. Illustration for Part Four Test Questions 6 through 8.

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7. Suppose you’re listening to music using the ampliﬁer whose speci-

ﬁcations include a graph such as that shown in Fig. Test 4-1. If

you increase the volume control setting by 2 units, the peak output

power, in watts, increases by

(a) 0.2 watts

(b) 0.4 watts

(d) 4 watts

(e) an amount that depends on the initial setting.

8. Suppose you’re listening to music using the ampliﬁer whose speci-

ﬁcations include a graph such as that shown in Fig. Test 4-1. If

you increase the volume control setting by 2 units, the peak output

power, in decibels, increases by

(a) 0.2 decibels

(b) 0.4 decibels

(d) 4 decibels

(e) an amount that depends on the initial setting

9. The sum of all the terms in a sequence is called

(a) a partial sum

(b) a series

(d) a geometric sequence

(e) a linear sequence

10. Which of the following is always a scalar quantity?

(a) The velocity of a train.

(b) The acceleration of a car.

(d) The mass of a truckload of bricks.

(e) The force produced by the wind against a wall.

11. Suppose you’re driving a motorboat across a river. The bow of the

boat is pointing straight south, and your water speed is 7 knots.

There is a steady current in the water moving from east to west at

a speed of 7 knots. What is your direction (heading) relative to land?

(a) South.

(b) Southeast.

(d) East.

(e) West.

Test: Part 4 387

12. Suppose you’re driving a motorboat across a river. The bow of the

boat is pointing straight north, and your water speed is 12 knots.

There is a steady current in the water moving from west to east at

a speed of 9 knots. What is your speed relative to land?

(a) 3 knots.

(b) 9 knots.

(d) 15 knots.

(e) It is impossible to tell without more information.

13. Suppose you buy a house for $200,000. You are conﬁdent that its

value will increase by exactly 10% per year for the next 10 years.

According to this formula, what should the house be worth after

3 years?

(a) $230,000

(b) $242,000

(d) $266,200

(e) More information is necessary to answer this question.

14. Suppose you buy a house for $200,000, and its value falls by exactly

10% per year for 3 years. What is the house worth at the end of the

3 years?

(a) $170,000

(b) $162,000

(d) $140,000

(e) More information is necessary to answer this question.

15. Which of the following can be expressed as a vector quantity?

(a) The mass of a bag of apples.

(b) The brightness of a source of light.

(d) The acceleration of a car.

(e) The volume of water in a swimming pool.

16. In Fig. Test 4-2, which of the vectors in the lower diagrams best

represents the velocity vector for the car shown in the top diagram?

Imagine the car moving generally from left to right along the road as

shown. Assume each division represents 5 meters per second.

(a) a

(b) b

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(d) d

(e) e

17. In Fig. Test 4-2, which of the vectors in the lower diagrams best

represents the acceleration vector for the car shown in the top

diagram? Imagine the car moving generally from left to right along

the road as shown. Assume each division represents 5 meters per

second squared.

(a) a

(b) b

(d) d

(e) e

18. Imagine the car reversing direction as shown in the diagram of

Fig. Test 4-2, so it moves generally from right to left at a constant

speed of 15 meters per second. Which of the vectors in the lower

Fig. Test 4-2. Illustration for Part Four Test Questions 16 through 18.

Test: Part 4 389

diagrams best represents the acceleration vector in this case? Assume

each division represents 5 meters per second squared.

(a) a

(b) b

(d) d

(e) e

19. Suppose Jimsville is 60 miles from Joesville. You need to get from

one town to the other in 90 minutes or less. Your minimum average

speed

(a) must be 30 miles per hour

(b) must be 40 miles per hour

(d) must be 60 miles per hour

(e) cannot be determined from this information

20. Suppose Jimsburg is 80 kilometers from Joesburg. You make a trip

from one town to the other in exactly 80 minutes. Your instanta-

neous acceleration

(a) must be at least 1 meter per second squared

(b) must be at least 60 meters per second squared

(d) must be at least 16.67 meters per second squared

(e) cannot be determined from this information

21. Suppose you deposit exactly $65,536.00 into an account on the ﬁrst

day of the month. On the second day of the month, you deposit

exactly half this amount. On the third day, you deposit half the

amount that you deposited on the second day. You repeat this

process until you can no longer cut the deposits in half while still

making them in whole cents (that is, without ‘‘breaking up a

penny’’). What will be the amount you have in the bank at that time?

(a) $131,071.75

(b) $131,071.00

(d) $131,072.00

(e) That time will never be reached; the account balance will con-

tinue to increase without limit.

22. Speed can be expressed in terms of

(a) distance multiplied by time

(b) distance per unit time

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