Chapter Three

"Which diagram below correctly represents A-B+2C?" (picture on eLearn) Select one: a. b. c. d. e. **all are pictures

a. **adding these vectors graphically gives: A-B+2C= 0

Which diagram below correctly represents A-B+2C? (eLearn picture) a. b. c. d. e.

a. 0 (just a dot in the origin)

"A child starts at one corner of a cubical jungle gym in a playground and climbs up to the diagonally opposite corner. The original corner is the coordinate origin, and the x, y and z axes are oriented along the jungle gym edges. The length of each side is 2 m." (look on eLearn for the picture) a. 2i + 2j + 2k b. 2.8i + 2.8j + 2.8k c. 2i + 2j + 2.8k d. 3.5i + 3.5j + 3.5k e. 2i + 2j + 3.5k

a. 2i + 2j + 2k

"Which of the following equation is the correct equation to find the y component of the A vector, given theta?" (eLearn picture below) select one: a. A sin (θ) b. A cos (θ) c. A tan (θ) d. Y cos (θ)

a. A sin (θ)

Which labeled vector equals the inverse (or opposite) of the red vector? Red-Vector.jpg Select one: a. E b. D c. A d. C e. B

a. E

What is the shape of a plot of the motion of a projectile (plotting y vs. t)? Select one: a. Parabolic b. Hyperbolic c. Linear d. Straight

a. Parabolic

Dana says any vector R can be represented as the sum of two vectors: R=A+B. Ardis says any vector R represented as the difference of two vectors: R=A-B. Which one, if either, is correct? Select one: a. They are both correct: A difference of vectors is a sum R=A + (-B) b. They are both wrong: Vectors can be moved as long as they keep the same magnitude and direction. c. Dana is correct: Any vector can be represented as a sum of components and not as a difference. d. Ardis is correct: Any vector can be represented as a difference of vector components and not as a sum. e. They are both wrong: every vector is unique.

a. They are both correct: A difference of vectors is a sum R=A + (-B)

Vectors are often split into two or more orthogonal components. What is true of these components in relation to each other? Select one: a. They are perpendicular. b. They are the same curvature. c. They are parallel. d. They are the same magnitude.

a. They are perpendicular.

When you add a velocity vector to a displacement vector you will find the ____ vector. Select one: a. You cannot add the displacement and velocity vectors. b. velocity c. displacement d. speed e. acceleration

a. You cannot add the displacement and velocity vectors.

Which of the following situations is the moving object considered a projectile? Select one: a. Your physics book tossed onto your desk b. An ascending airplane c. A blown soap bubble after leaving the wand. d. A rocket leaving the launch pad

a. Your physics book tossed onto your desk

Express vector u in terms of a, b, and c. (bigger eLearn picture) a. a-b-c b. -a-b-c c. -a+b-c d. a+b+c

a. a-b-c

When aiming at a distant target with a bow and arrow, you should aim ________ the bulls-eye. (Assume there is no wind and the target will be hit sometime after the arrow reaches the apex of the motion.) Select one: a. above b. below c. to the left of d. to the right of e. directly at

a. above

In the last moments of a basketball game, the ball is lobbed by a desperate player across the court towards the basket. When the ball reaches it's maximum height, what can you say about the vertical component of the ball's velocity? Select one: a. It is zero. b. It is also at its maximum. c. It is not changing.

a. it is zero

"The vector A→ has components +5 and +7 along the x and y axes respectively. If the vector is now rotated 90 degrees counterclockwise relative to the original axes, the vector's components are now..." Select one: a. -7; 0. b. -7; 5. c. -7; -5. d. 7; -5. e. 7; 5.

b. -7; 5. **The original x position is x = +5. When this is rotated 90º counterclockwise from the + x-axis, it now is along the y-axis but now at y = +5. The original y position is y = +7. When this is rotated 90º counterclockwise from the + y-axis, it now is along the - x-axis but now at x = -7.

Which vector is the opposite of A? That is, the same magnitude as A, but the opposite direction. Select one: a. |A| b. -A c. A d. A+A

b. -A

"An African swallow is carrying a coconut. It drops the coconut during flight. Define the +x-direction as the same direction as the bird is flying and the +y direction as up. What is the value of the vertical component of acceleration for the coconut once released?" select one: a. 6 m/s^2 b. -g c. g d. -g/2 e. g/2

b. -g **since we have defined down as negative, the vertical acceleration is -g

After a quarterback throws a football down-field, the horizontal acceleration (neglecting air resistance) of the ball is Select one: a. 9.8 m/s^2 upfield b. 0 m/s^2 c. 1/2(9.8) m/s^2 downfield d. 1/2 (9.8) m/s^2 upfield e. 9.8 m/s^2 downfield

b. 0 m/s^2

How many address values (x, y, z, r, θ, ect.)are required to define the location of a point on a given plane. Select one: a. 4 b. 2 c. 1 d. 3

b. 2

How many different vectors are drawn here ? (picture on eLearn) select one: a. 1 b. 2 c. 3 d. 4 e. 5

b. 2

"A projectile is launched on the Earth with a certain initial velocity and moves without air resistance. Another projectile is launched with the same initial velocity on the Moon, where the acceleration due to gravity is one-sixth as large. How does the range of the projectile on the Moon compare with that of the projectile on the Earth?" Select one: a. It is the same b. It is 6 times larger. c. It is √6 times larger d. It is 36 times larger. e. It is one-sixth as large

b. It is 6 times larger. **use the range equation R=(v^2isin2(θi))/g. On the moon the gravitational acceleration is g/6. Thus the range on the moon is R=6(v^2isin2(θi))/g

What does the length of a vector indicate? Select one: a. The sign. b. The magnitude. c. The direction. d. The color.

b. The magnitude.

"As a projectile moves in its parabolic path, the velocity and acceleration vectors are perpendicular to each other _______." Select one: a. nowhere along the projectile's path. b. at the peak of its path. c. not enough information is given. d. everywhere along the projectile's path.

b. at the peak of its path. **At the top of the path (in between rising and descending), the velocity vector is horizontal. This is because the vertical component of velocity is zero. The acceleration vector is always pointed down due to gravity. (picture on eLearn if needed)

"The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by r= (1.61*10^6i + 9.14*10^3j)m and v=(+224i) m/s. The plane is most likely...." select one: a. just touching down. b. in level flight in the air. c.ascending d. descending. e. taking off.

b. in level flight in the air.

"A projectile is launched on the Earth with a certain initial velocity and moves without air resistance. Another projectile is launched with the same initial velocity on the Moon, where the acceleration due to gravity is one-sixth as large. How does the maximum height of the projectile on the Moon compare with that of the projectile on the Earth?" Select one: a. It is 36 times larger. b. It is 6 times larger. Correct c. It is √6 times larger d. It is the same e. It is one-sixth as large

b. it is 6 times larger **Use the Maximum Height Equation R=(v^2isin2(θi))/g. On the moon the gravitational acceleration is g/6. Thus the range on the moon is R=6(v^2isin2(θi))/g.

Express vector u in terms of a, b, and c. (smaller eLearn picture) a. a+b+c b. a+b-c c. -a-b-c d. -a+b-c

c. -a-b-c

"What is the angle between the vectors A→ and −A→ when they are drawn from a common origin?" select one: a. 0 degrees b. 90 degrees c. 180 degrees d. 270 degrees e. 360 degrees

c. 180 degrees **vectors pointed in opposite directions are separated by 180 degrees

"Vector D→ in the drawing below is equal to __________ ?" (look on eLearn for the drawing) select one: a. C+F b. B+D+F c. A+B d. A+C e. B+C

c. A+B

A block is supported on a compressed spring, which projects the block straight up in the air at velocity v⃗ =viyj^v→=viyj^. The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block.) Select one: a. At the instant when the block leaves the spring, directed at the block. b. At the instant when the block leaves the spring, directed at the spring. c. At the instant when the block is at the highest point, directed at the block d. At the instant when the block is at the highest point, directed at the spring. e. When the block is back at the spring's original position, directed at that position.

c. At the instant when the block is at the highest point, directed at the block

If vector B⃗ B→ is added to vector A⃗ A→, which of the following must be true for the resultant vector to be equal to zero? Select one: a. A⃗ A→ and B⃗ B→ are perpendicular b. A⃗ A→ and B⃗ B→ are parallel and in the same direction & equal in magnitude c. A⃗ A→ and B⃗ B→ are parallel and in the opposite direction & equal in magnitude d. A⃗ A→ and B⃗ B→ are parallel and in the same direction & different in magnitude e. A⃗ A→ and B⃗ B→ are perpendicular and equal in magnitude f. A⃗ A→ and B⃗ B→ are equal in magnitude alone

c. A⃗ A→ and B⃗ B→ are parallel and in the opposite direction & equal in magnitude

"Two balls, projected at different times so they don't collide, have trajectories A and B, as shown below. (eLearn picture below) Which statement is correct?" select one: a. v0B must be greater than v0A. b. Ball A is in the air for a longer time than ball B. c. Ball B is in the air for a longer time than ball A. d. Ball B has a greater acceleration than ball A. e. Ball A has a greater acceleration than ball B.

c. Ball B is in the air for a longer time than ball A.

Given the statement that A-B = -A+C, what can we conclude? a. C=A b. 2A = B+C c. C= -B d. A=B

c. C=-B

"How do you add two vectors graphically?" select one: a. This can't be done; vectors can only be added algebraically. b. Place them tail-to-tail and draw the addition vector connecting the two heads. c. Place them head-to-tail and draw the addition vector from the tail of the first to the head of the second. d. Place them head-to-tail and draw the addition vector from the tail of first to the tail of the second.

c. Place them head-to-tail and draw the addition vector from the tail of the first to the head of the second.

"The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by r= (1.61*10^6i + 3.00*10^3j)m and v=(150i +21j) m/s. The plane is most likely...." select one: a. just touching down. b. in level flight in the air. c.ascending d. descending. e. taking off.

c. ascending **the vertical component (j component) is positive, but not as large as the horizontal component

"You are on a humanitarian mission to drop needed supplies to a group of people stranded in a narrow canyon. You need to push the supplies out of the plane _______ the canyon. (Assume there is no wind.)" select one: a. directly over b. just after passing c. before you reach

c. before you reach **The package has horizontal velocity due to the horizontal movement of the plane. Since no force counteracts this horizontal velocity, the package will move horizontally at the same speed as the plane.

Which one of the following choices is a vector quantity? Select one: a. mass b. distance c. displacement d. volume e. time f. temperature

c. displacement

Two cooks standing side by side in a restaurant pull their beaters out of the dough at the same instant. A glob of dough flies off each beater. Each glob lands on the top of a tin the same horizontal distance away and at its initial height. However, one lands later than the other. The explanation is that they left the beaters at angles q1 and q2 such that: Select one: a. q2 = -q1. b. q1 + q2 = π/4 c. q1 + q2 = π/2 d. q1 + q2 = p. e. q1 - q2 = p. ***q= theta

c. q1 + q2 = π/2

Which of the following vectors shows non-zero displacement in both the x and y directions? (I cannot make the answers in bold font, so assume that the r, i, and j represent vectors) Select one: a. r = 2 i + 0 j b. r = 0 i + 3 j c. r = 2 i + 3 j

c. r = 2 i + 3 j

Robin Hood shoots an arrow up in the night sky. What is the acceleration at the very top of its path? Select one: a. 9.80 m/s2 upward b. zero c. it depends on the initial velocity d. 9.80 m/s2 downward

d. 9.80 m/s2 downward

The diagram below shows 3 vectors which sum to zero, all of equal length. Which statement below is true? (eLearn picture) select one: a. A+B = A-C b. A-B = 2A + C c. 2A + 2B = 2C d. A-B = 2A + C e. A+B = B-C

d. A-B = 2A + C

With the x axis horizontal and the y axis vertically upward, the change in the horizontal component of velocity, Dvx, and the change in the vertical component of velocity, Dvy, of a projectile are related to the time since leaving the barrel, Dt, as Select one: a. Dvx = 0; Dvy = 0. b. Dvx = gDt; Dvy = 0. c. Dvx = 0; Dvy = gDt. d. Dvx = 0; Dvy = -gDt. e. Dvx = gDt; Dvy = -gDt. **D=delta

d. Dvx = 0; Dvy = -gDt.

Which statement is true about the unit vectors i^, j^ and k^? Select one: a. Each has a length of 1 m. b. Their directions are defined by a left-handed coordinate system. c. If i^ is directed east and j^ is directed south, k^ points up out of the surface. d. The angle between any two is 90 degrees

d. The angle between any two is 90 degrees

Consider the following controls in an automobile: - gas pedal, - brake, - steering wheel. What are the controls in this list that cause an acceleration of the car? Select one: a. only the steering wheel b. the gas pedal and the brake c. only the brake d. all three controls e. the steering wheel and the gas pedal f. the steering wheel and the brake g. only the gas pedal

d. all three controls

"Two identical heavy metal spheres are released from the same height. Sphere 1 is at rest, and sphere 2 has a velocity of 10 m/s in horizontal direction." select one: a. Sphere 2 will take about 10% longer than sphere 1 to hit the ground. b. Sphere 1 will take much longer than sphere 2 to hit the ground. c. Sphere 2 will take much longer than sphere 1 to hit the ground. d. Both spheres hit the ground at the same time.

d. both spheres hit the ground at the same time **the horizontal velocity does not impact the flight time

"The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by r= (1.61*10^6i + 3.00*10^3j)m and v=(150i-21j) m/s. The plane is most likely...." select one: a. just touching down. b. in level flight in the air. c.ascending d. descending. e. taking off.

d. descending.

Which one of the following choices is a vector quantity? Select one: a. volume of a gallon of milk b. the age of the earth c. attendance at a baseball game d. the earth's pull on your body e. the mass of a football f. the temperature of an iron bar

d. the earth's pull on your body

A projectile starts at the coordinate origin, where the displacement vector also originates. The initial velocity, v0, makes an angle q0 with the horizontal where 0 < q0 < 90°. At the instant when the projectile is at the highest point of its trajectory, the displacement, velocity and acceleration vectors are r⃗ r→, v⃗ v→ and a⃗ a→. Which statement is true? Select one: a. r⃗ r→ is parallel to v⃗ v→. b. r⃗ r→ is perpendicular to v⃗ v→. c. v⃗ v→ is parallel to a⃗ a→. d. v⃗ v→ is perpendicular to a⃗ a→. e. r⃗ r→ is perpendicular to a⃗ a→.

d. v is perpendicular to a

"In projectile motion what is the horizontal acceleration?" select one: a. g b. 6 m/s^2 c. g/2 d. zero. e. -g

d. zero **Since there are no forces (like gravity) acting on the horizontal direction, there is no acceleration in this direction.

Which labeled vector equals the red vector? Select one: a. D b. E c. C d. B e. A

e. A

A vector lying in the xy-plane has components with opposite signs. The vector must lie in which quadrant? Select one: a. the first quadrant only b. the second quadrant only c. either the first or third quadrant d. the fourth quadrant only e. either the second or fourth quadrant f. the third quadrant only

e. either the second or fourth quadrant

Which diagram below correctly represents A+B+C? (eLearn picture) a. b. c. d. e.

e. line going at a slant linearly

Given the lengths of two sides of a triangle, you can then determine any of the angles of the triangle. Select one: True False

false

Temperature can be written as a vector quantity. Select one: True False

false

The x-component of a vector can be longer than the vector itself. Select one: True False

false

Two projectiles are thrown upward in the air with the same initial speed, one at an angle of θ with respect to the level ground and the other at an angle of 90o - θ. Both projectiles strike the ground at the same distance from the launch point. Both projectiles are in the air for the same amount of time. Select one: True False

false

When adding vectors it does NOT matter which order you add them. Select one: True False

true