Question 1

Express the polar vector (22;124S1U1P1$\circ$S1S1P0)in unit vector notation.

Accepted Answer

A) 18.2i - 12.3j 
B) -12.3i + 18.2j 
C) 12.3i - 18.2j 
D) 12.3i + 18.2j 
E) -18.2i + 12.3j 
A) 18.2i - 12.3j 
B) -12.3i + 18.2j 
C) 12.3i - 18.2j 
D) 12.3i + 18.2j 
E) -18.2i + 12.3j

Question 2

The width of the nail of you thumb is approximately equal to which of the following units:

Accepted Answer

A) 1 $\mu$m. 
B) 1 mm. 
C) 1 cm. 
D) 1 m. 
E) 1 km. 
A) 1 $\mu$m. 
B) 1 mm. 
C) 1 cm. 
D) 1 m. 
E) 1 km.

Question 3

A man walks 15 m due east,then makes a sharp left turn and walks 23 m due north and then climbs up a vertical ladder to the top of 6 m high structure.Calculate the total displacement of the man.

Accepted Answer

A) 36 m 
B) 44 m 
C) 28 m 
D) 33 m 
E) None are correct. 
A) 36 m 
B) 44 m 
C) 28 m 
D) 33 m 
E) None are correct.

Question 4

If you head at a compass heading of 15S1U1P1$\circ$S1S1P0 for 25 m,then go on a heading of 280S1U1P1$\circ$S1S1P0 for 18 m,how far are you from your starting point?

Accepted Answer

A) 15 m 
B) 29 m 
C) 32 m 
D) 38 m 
A) 15 m 
B) 29 m 
C) 32 m 
D) 38 m

Question 5

A sphere and a cube have the same volume.If the radius of the sphere is 5.00 cm,then what is the area of one side of the cube?

Accepted Answer

A) 25.0 cm2 
B) 65.0 cm2 
C) 105 cm2 
D) 125 cm2 
A) 25.0 cm2 
B) 65.0 cm2 
C) 105 cm2 
D) 125 cm2

Question 6

The volume of a rectangular block of width w = 116.5 cm,depth d = 164.8 cm,and height h = 105.1 cm is (given in scientific notation and with the correct number of significant figures):

Accepted Answer

A) 2.018 * 106 cm3 
B) 2.02 * 106 cm3 
C) 2.0178 * 106 cm3 
D) 2.0 * 106 cm3 
E) 2.01784 * 106 cm3 
A) 2.018 * 106 cm3 
B) 2.02 * 106 cm3 
C) 2.0178 * 106 cm3 
D) 2.0 * 106 cm3 
E) 2.01784 * 106 cm3

Question 7

27500 people live in the Duchy of Grand Fenwick,which has a land area of a square 5.8 km on each side.How many people live there per square km?

Accepted Answer

A) 820 
B) 817 
C) 810 
D) 809 
A) 820 
B) 817 
C) 810 
D) 809

Question 8

A vector   with magnitude 25.0 m points along the negative x direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

Accepted Answer

A) Ax = 25.0 cos 50.0S1U1P1$\circ$S1S1P0 and Ay = 25.0 sin 50.0S1U1P1$\circ$S1S1P0 
B) Ax = 25.0 sin 50.0S1U1P1$\circ$S1S1P0 and Ay = 25.0 cos 50.0S1U1P1$\circ$S1S1P0 
C) Ax = 25.0 sin 230S1U1P1$\circ$S1S1P0 and Ay = 25.0 cos 230S1U1P1$\circ$S1S1P0 
D) Ax = 25.0 cos 230S1U1P1$\circ$S1S1P0 and Ay = 25.0 sin 230S1U1P1$\circ$S1S1P0 
A) Ax = 25.0 cos 50.0S1U1P1$\circ$S1S1P0 and Ay = 25.0 sin 50.0S1U1P1$\circ$S1S1P0 
B) Ax = 25.0 sin 50.0S1U1P1$\circ$S1S1P0 and Ay = 25.0 cos 50.0S1U1P1$\circ$S1S1P0 
C) Ax = 25.0 sin 230S1U1P1$\circ$S1S1P0 and Ay = 25.0 cos 230S1U1P1$\circ$S1S1P0 
D) Ax = 25.0 cos 230S1U1P1$\circ$S1S1P0 and Ay = 25.0 sin 230S1U1P1$\circ$S1S1P0

Question 9

How many significant figures are in the number 0.00640?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 5 
A) 1 
B) 2 
C) 3 
D) 4 
E) 5

Question 10

Approximately how many water molecules are in one liter of water? One mole contains 6.02 * 1023 molecules,the density of water is 1.00∙103 grams/liter and the mass of one mole of water is 18.0 grams.

Accepted Answer

A) 6.02 * 1023 
B) 3.34 * 1025 
C) 6.02 * 1026 
D) 1.08 * 1028 
A) 6.02 * 1023 
B) 3.34 * 1025 
C) 6.02 * 1026 
D) 1.08 * 1028

Question 11

If vector   and vector   ,where   and   are the units vectors along the x and the y directions respectively,calculate the magnitude of vector   .

Accepted Answer

A) 10.3 
B) 17.4 
C) -6.7 
D) 26 
E) -12.3 
A) 10.3 
B) 17.4 
C) -6.7 
D) 26 
E) -12.3

Question 12

A sphere and a cube have the same volume.If the the edge of one side of the cube is 5.00 cm,then what is the surface area of the sphere?

Accepted Answer

A) 25.0 cm2 
B) 121 cm2 
C) 150.0 cm2 
D) 105 cm2 
A) 25.0 cm2 
B) 121 cm2 
C) 150.0 cm2 
D) 105 cm2

Question 13

Kobe Bryant of the LAL (LA Lakers)is 6'6" tall.His height in meters is

Accepted Answer

A) 6.2 m. 
B) 3.5 m. 
C) 2.9 m. 
D) 1.98 m. 
A) 6.2 m. 
B) 3.5 m. 
C) 2.9 m. 
D) 1.98 m.

Question 14

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m3?

Accepted Answer

A) 4.53 m 
B) 9.50 m 
C) 12.67 m 
D) 19.00 m 
A) 4.53 m 
B) 9.50 m 
C) 12.67 m 
D) 19.00 m

Question 15

Three vectors are all in the same plane,they have equal magnitudes and make 120S1U1P1$\circ$S1S1P0 angles with each other.We can say that

Accepted Answer

A) the magnitude of their resultant is three times the magnitude of each component vector. 
B) the magnitude of their resultant is more than three times the magnitude of each component vector. 
C) the magnitude of their resultant is one-third the magnitude of the component vectors. 
D) the magnitude of their resultant is zero. 
E) the magnitude of their resultant is equal to the magnitude of the component vectors. 
A) the magnitude of their resultant is three times the magnitude of each component vector. 
B) the magnitude of their resultant is more than three times the magnitude of each component vector. 
C) the magnitude of their resultant is one-third the magnitude of the component vectors. 
D) the magnitude of their resultant is zero. 
E) the magnitude of their resultant is equal to the magnitude of the component vectors.

Question 16

What are the polar coordinates of the vector 3i-2j?

Accepted Answer

A) (3.6;33.7S1U1P1$\circ$S1S1P0) 
B) (3.6;146.3S1U1P1$\circ$S1S1P0) 
C) (4.2;33.7S1U1P1$\circ$S1S1P0) 
D) (4.2;-33.7S1U1P1$\circ$S1S1P0) 
E) (3.6;-33.7S1U1P1$\circ$S1S1P0) 
A) (3.6;33.7S1U1P1$\circ$S1S1P0) 
B) (3.6;146.3S1U1P1$\circ$S1S1P0) 
C) (4.2;33.7S1U1P1$\circ$S1S1P0) 
D) (4.2;-33.7S1U1P1$\circ$S1S1P0) 
E) (3.6;-33.7S1U1P1$\circ$S1S1P0)

Question 17

What is the magnitude of the vector   ?

Accepted Answer

A) 2.0 
B) 6.0034 
C) 7.2 
D) 10 
E) 24 
A) 2.0 
B) 6.0034 
C) 7.2 
D) 10 
E) 24

Question 18

Assume that the mass of any cell in the human body is 5 * 10-15 kg.If Alice has a mass of 50 kg how many cells are there in her body?

Accepted Answer

A) 1017 cells 
B) 1016 cells 
C) 1015 cells 
D) 1014 cells 
E) 1013 cells 
A) 1017 cells 
B) 1016 cells 
C) 1015 cells 
D) 1014 cells 
E) 1013 cells

Question 19

Given two vectors,   and   :     What is the magnitude of the vector   ?

Accepted Answer

A) 15.3 
B) 17.6 
C) 18.8 
D) 19.0 
E) 20.0 
A) 15.3 
B) 17.6 
C) 18.8 
D) 19.0 
E) 20.0

Question 20

The fraction of a kilogram in a milligram is

Accepted Answer

A) 10-6. 
B) 10-4. 
C) 10-3. 
D) 10-2. 
A) 10-6. 
B) 10-4. 
C) 10-3. 
D) 10-2.

Exam 1: Overview

Express the polar vector (22;124 ∘\circ∘ )in unit vector notation.

The width of the nail of you thumb is approximately equal to which of the following units:

A man walks 15 m due east,then makes a sharp left turn and walks 23 m due north and then climbs up a vertical ladder to the top of 6 m high structure.Calculate the total displacement of the man.

If you head at a compass heading of 15 ∘\circ∘ for 25 m,then go on a heading of 280 ∘\circ∘ for 18 m,how far are you from your starting point?

A sphere and a cube have the same volume.If the radius of the sphere is 5.00 cm,then what is the area of one side of the cube?

The volume of a rectangular block of width w = 116.5 cm,depth d = 164.8 cm,and height h = 105.1 cm is (given in scientific notation and with the correct number of significant figures):

27500 people live in the Duchy of Grand Fenwick,which has a land area of a square 5.8 km on each side.How many people live there per square km?

A vector with magnitude 25.0 m points along the negative x direction.If it is rotated by 50.0 degrees counterclockwise,what are the components of the vector?

How many significant figures are in the number 0.00640?

Approximately how many water molecules are in one liter of water? One mole contains 6.02 * 1023 molecules,the density of water is 1.00∙103 grams/liter and the mass of one mole of water is 18.0 grams.

If vector and vector ,where and are the units vectors along the x and the y directions respectively,calculate the magnitude of vector .

A sphere and a cube have the same volume.If the the edge of one side of the cube is 5.00 cm,then what is the surface area of the sphere?

Kobe Bryant of the LAL (LA Lakers)is 6'6" tall.His height in meters is

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m3?

Three vectors are all in the same plane,they have equal magnitudes and make 120 ∘\circ∘ angles with each other.We can say that

What are the polar coordinates of the vector 3i-2j?

What is the magnitude of the vector ?

Assume that the mass of any cell in the human body is 5 * 10-15 kg.If Alice has a mass of 50 kg how many cells are there in her body?

Given two vectors, and : What is the magnitude of the vector ?

The fraction of a kilogram in a milligram is

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Express the polar vector (22;124^$\circ$)in unit vector notation.

If you head at a compass heading of 15^$\circ$ for 25 m,then go on a heading of 280^$\circ$ for 18 m,how far are you from your starting point?

Approximately how many water molecules are in one liter of water? One mole contains 6.02 * 10²³ molecules,the density of water is 1.00∙10³ grams/liter and the mass of one mole of water is 18.0 grams.

What is the sum of the lengths of all the edges of a cube whose volume is 3.97 m³?

Three vectors are all in the same plane,they have equal magnitudes and make 120^$\circ$ angles with each other.We can say that

Assume that the mass of any cell in the human body is 5 * 10^-15 kg.If Alice has a mass of 50 kg how many cells are there in her body?