PHYSICS LEVEL 2
Name _______________________________________________________
Period _______________
INTRODUCTION TINKHAM QUESTIONS
1. You can always add two numbers that have the same units. However, you cannot always add two
numbers that have the same dimensions. Explain why not; include an example in your explanation.
2. The following table lists four variables along with their units:
Variable
Units
x
meters (m)
v
meters per second (m/s)
t
seconds (s)
a
meters per second squared (m/s2)
These variables appear in the following equations, along with a few numbers that have no units. In
which of the equations are the units on the left side of the equals sign consistent with the units on the
right side?
a. x  vt
d. v  at  12 at 3
b. x  vt  12 at 2
e. v3  2ax 2
c. v  at
f. t 
2x
a
3. Is it possible for two quantities to have the same dimensions but different units? Support your answer
with an example and an explanation.
4. Is it possible for two quantities to have the same units but different dimensions? Support your answer
with an example and an explanation.
5. A student sees a newspaper ad for an apartment that has 1330 square feet (ft2) of floor space. How
many square meters of area are there?
6. Suppose a man’s scalp hair grows at a rate of 0.35 mm per day. What is this growth rate in feet per
century?
7. Given the quantities a = 9.7 m, b = 4.2 s, and c = 69 m/s, what is the value with units of the quantity
d = a3/(cb2)?
8. Estimate the number of breaths taken by a person over 70 years assuming the person takes one breath
every 8 seconds.
9. A partly full paint can has 0.67 U.S. gallons of paint left in it. What is the volume of the paint in
cubic meters?
10. Estimate the number of times your heart beats in 1 day if it beats 72 times every minute.
11. How many seconds old is a person who is 17 years old?
12. The depth of the ocean is sometimes measured in fathoms (1 fathom = 6 feet). Distance on the
surface of the ocean is sometimes measured in nautical miles (1 nautical mile = 6076 feet).
a. Convert 1.20 nautical miles to meters.
b. Convert 2.60 nautical miles to meters.
c. Convert the depth 16.0 fathoms to meters.
13. Azelastine hydrochloride is an antihistamine nasal spray. A standard size container holds one fluid
ounce of the liquid. You are searching for this medication in a European drugstore and are asked how
many milliliters there are in one fluid ounce. Using the following conversion factors, determine the
number of milliliters in a volume of one fluid ounce:
1 gal = 128 oz
3.785 x 10-3 m3 = 1 gal
1 mL = 10-6 m3
14. Which of the following quantities (if any) can be considered a vector? Explain your reasoning.
a. the number of people attending a football game
b. the number of days in a month
c. the number of pages in a book?
15. Are two vectors with the same magnitude necessarily equal? Give your reasoning.
16. Can two nonzero perpendicular vectors be added together so their sum is zero? Explain.
17. Can three or more vectors with unequal magnitudes be added together so their sum is zero? If so,
show by means of a tail-to-head arrangement of the vectors how this could occur.
18. Vectors A and B satisfy the vector equation A + B = 0.
a. How does the magnitude of B compare with the magnitude of A? Give your reasoning.
b. How does the direction of B compare with the direction of A? Give your reasoning.
19. Vectors A, B, and C satisfy the vector equation A + B = C, and their magnitudes are related by the
scalar equation A2  B2  C 2 . How is vector A oriented with respect to vector B? Account for your
answer.
20. Vectors A, B, and C satisfy the vector equation A + B = C, and their magnitudes are related by the
scalar equation A  B  C . How is vector A oriented with respect to vector B? Explain your reasoning.
21. On her trip home from school, Karla drives along three streets after exiting the driveway. She drives
1.85 miles south, 2.43 miles east, and 0.35 miles north. What is Karla’s resultant displacement in miles?
Include a vector diagram.
22. Brady makes a pass 25 yds directly to the right to Gronkowski, who catches it and runs 50 yds
directly downfield for a touchdown. What is the ball’s resultant displacement? Include a vector
diagram.
23. Using your calculator, verify that sin divided by cos is equal to tan , for an angle  . Try 30,
for example. Prove that this result is true in general by using the definition for sin , cos , and tan .
24. Is it possible for one component of a vector to be zero, while the vector itself is not zero? Explain.
25. Is it possible for a vector to be zero, while one component of the vector is not zero? Explain.
26. A displacement vector has an x-component of -125 m and a y-component of -184 m. What is its
magnitude and angle?
27.Which of the following displacement vectors (if any) are equal? Explain your reasoning.
Vector
Magnitude
Direction
100 m
A
30 north of east
100 m
B
30 south of west
50 m
C
30 south of west
100 m
D
60 east of north
28. Two ropes are attached to a heavy box to pull it along the floor. One rope applies a force of 475 N
in a direction due west; the other applies a force of 315 N in a direction due south. What is the
magnitude and angle of the resultant force? Include a vector diagram, which will be a top view of the
box.
29. You are on a treasure hunt and your map says “Walk due west for 52 paces, then walk 30 north of
west for 42 paces, and finally walk due north for 25 paces.” What are the components of the resultant
displacement in paces? Include a vector diagram.