Q: A vector $$\\vec{A}$$ has a magnitude of 5 units and points 30° above the positive x-axis. What are its x- and y-components?

$$A_x = 5 \\cos(30^\\circ), \\ A_y = 5 \\sin(30^\\circ)$$

Q: Which of the following statements about vector addition is correct?

$$\\vec{A} + \\vec{B} = \\vec{B} + \\vec{A}$$

Q: A projectile is launched with an initial velocity $$v_0 at an $$angle $$\\theta$$ above the horizontal. What is the initial vertical component of velocity?

$$v_{0y} = v_0$ \\sin \\theta$$

Q: Which of the following is the correct equation for the vertical displacement $$y of a $$projectile launched with initial vertical velocity $$v_{0y}$$ and vertical acceleration $$a_y$$ after time $$t$$?

$$y = v_{0y} t + \\frac{1}{2} a_y t^2$

Q: Which of the following is a correct representation of a vector $$\\vec{A} in $$terms of unit vectors?

$$\\vec{A} = A_x \\hat{i} + A_y \\hat{j}$$

Q: A soccer ball is kicked with an initial speed of 20 m/s at an angle of 45° above the horizontal. What is the initial vertical velocity?

$$v_{0y} = 20 \\sin(45^\\circ)$$

Q: A vector $$\\vec{D}$$ has components $$D_x = 8$$ and $$D_y = -6. $$What is the magnitude of $$\\vec{D}$$?

$$\\sqrt{8^2$ + (-6)^2$} = 10$$

Question 1

Which of the following is a vector quantity?

Accepted Answer

Displacement

Question 2

A vector $$\vec{A}$$ has a magnitude of 5 units and points 30° above the positive x-axis. What are its x- and y-components?

Accepted Answer

$$A_x = 5 \cos(30^\circ), \ A_y = 5 \sin(30^\circ)$$

Question 3

Which rule is used to graphically add two vectors by placing the tail of one at the tip of the other?

Accepted Answer

Tip-to-tail rule

Question 4

A hiker walks 4 km east and then 3 km north. What is the magnitude of the net displacement?

Accepted Answer

$$\sqrt{4^2$ + 3^2$} = 5 km$$

Question 5

Which of the following statements about vector addition is correct?

Accepted Answer

$$\vec{A} + \vec{B} = \vec{B} + \vec{A}$$

Question 6

A projectile is launched with an initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin \theta$$

Question 7

A ball is thrown horizontally from a cliff. Neglecting air resistance, which statement is true about its horizontal and vertical motions?

Accepted Answer

The horizontal and vertical motions are independent of each other

Question 8

Given a vector $$\vec{A}$$ with components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$

Question 9

A car rounds a curve and its velocity changes direction but not magnitude. What does this indicate about its acceleration?

Accepted Answer

There is acceleration because velocity direction changes

Question 10

A vector $$\vec{B}$$ has magnitude 10 units and points 60° above the positive x-axis. What is $$B_x$$?

Accepted Answer

$$B_x = 10 \cos(60^\circ)$$

Question 11

Which of the following is the correct equation for the vertical displacement $$y of a $$projectile launched with initial vertical velocity $$v_{0y}$$ and vertical acceleration $$a_y$$ after time $$t$$?

Accepted Answer

$$y = v_{0y} t + \frac{1}{2} a_y t^2$

Question 12

A vector $$\vec{C}$$ has components $$C_x = -2$$ and $$C_y = 6. $$What is the direction of $$\vec{C}$$ measured counterclockwise from the positive x-axis?

Accepted Answer

$$\theta = \arctan(6/(-2))$$

Question 13

Which of the following is a correct representation of a vector $$\vec{A} in $$terms of unit vectors?

Accepted Answer

$$\vec{A} = A_x \hat{i} + A_y \hat{j}$$

Question 14

A projectile is launched horizontally from a height $$h$$ with initial speed $$v_0. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 15

If a vector $$\vec{A} is $$subtracted from vector $$\vec{B}$$, which of the following correctly represents the operation?

Accepted Answer

$$\vec{B} - \vec{A}$$

Question 16

A soccer ball is kicked with an initial speed of 20 m/s at an angle of 45° above the horizontal. What is the initial vertical velocity?

Accepted Answer

$$v_{0y} = 20 \sin(45^\circ)$$

Question 17

Which of the following is true about the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

The acceleration is constant and downward

Question 18

A vector $$\vec{D}$$ has components $$D_x = 8$$ and $$D_y = -6. $$What is the magnitude of $$\vec{D}$$?

Accepted Answer

$$\sqrt{8^2$ + (-6)^2$} = 10$$

Question 19

A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the equation for its horizontal displacement after time $$t$$?

Accepted Answer

$$x = v_0$ \cos \theta \cdot t$$

Vectors and Motion in Two Dimensions

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