Q: A ball is thrown vertically upward with an initial velocity of $$10\ \text{m/s}. $$Using Chapter 2.4-2.7 concepts, what is its maximum height? (Assume $$g = 9.8\ \text{m/s}^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 \times 9.8} \approx 5.1\ \text{m}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its horizontal range according to Chapter 2.4-2.7?

$$R = \frac{v_0$^2 \sin 2\theta}{g}$$

Q: A cyclist travels 20 km east and then 15 km north. What is the magnitude of the displacement vector according to Chapter 3.1-3.3?

$$\sqrt{(20)^2$ + (15)^2$} = 25\ \text{km}$$

Q: A student drops a stone from a bridge. How long does it take to hit the ground 45 m below? (Use $$g = 9.8\ \text{m/s}^2$$ and Chapter 2.1-2.3 equations)

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} \approx 3.03\ \text{s}$$

Q: A runner increases her velocity from $$2\ \text{m/s} to$$ $$6\ \text{m/s} in$$ $$4\ \text{s}. $$What is her average acceleration? (Chapter 2.1-2.3)

$$a = \frac{v - v_0$}{t} = \frac{6 - 2}{4} = 1\ \text{m/s}^2$$

Question 1

Which of the following best describes the scientific method as reviewed in Chapter 1?

Accepted Answer

A process involving observation, hypothesis formation, experimentation, and revision.

Question 2

A car accelerates from rest at a constant rate. Which equation from Chapter 2.1-2.3 would you use to find its velocity after time $$t$$?

Accepted Answer

$$v = v_0$ + at$$

Question 3

A ball is thrown vertically upward with an initial velocity of $$10\ 	ext{m/s}. $$Using Chapter 2.4-2.7 concepts, what is its maximum height? (Assume $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 	imes 9.8} \approx 5.1\ 	ext{m}$$

Question 4

Which of the following is NOT a vector quantity as discussed in Chapter 3.1-3.3?

Accepted Answer

Speed

Question 5

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its horizontal range according to Chapter 2.4-2.7?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g}$$

Question 6

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is the magnitude of their dot product as covered in Chapter 3.1-3.3?

Accepted Answer

$$\vec{A} \cdot \vec{B} = 0$$

Question 7

A cyclist travels 20 km east and then 15 km north. What is the magnitude of the displacement vector according to Chapter 3.1-3.3?

Accepted Answer

$$\sqrt{(20)^2$ + (15)^2$} = 25\ 	ext{km}$$

Question 8

Which equation best describes the relationship between position, velocity, and acceleration for constant acceleration as discussed in Chapter 2.1-2.3?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 9

A student drops a stone from a bridge. How long does it take to hit the ground 45 m below? (Use $$g = 9.8\ 	ext{m/s}^2$$ and Chapter 2.1-2.3 equations)

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} \approx 3.03\ 	ext{s}$$

Question 10

Which of the following statements about acceleration is correct according to Chapter 1 review?

Accepted Answer

Acceleration is the rate of change of velocity with respect to time.

Question 11

A runner increases her velocity from $$2\ 	ext{m/s} to$$ $$6\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is her average acceleration? (Chapter 2.1-2.3)

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{6 - 2}{4} = 1\ 	ext{m/s}^2$$

Question 12

Which formula would you use to find the final velocity of an object given its initial velocity, acceleration, and displacement? (Chapter 2.4-2.7)

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 13

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is its magnitude? (Chapter 3.1-3.3)

Accepted Answer

$$|\vec{A}| = \sqrt{A_x^2$ + A_y^2$} = 5$$

Question 14

Which of the following best describes the difference between displacement and distance as discussed in Chapter 1 review?

Accepted Answer

Displacement is a vector quantity, while distance is a scalar quantity.

Question 15

A projectile is launched horizontally from a cliff. Which equation describes its vertical position after time $$t$$? (Chapter 2.4-2.7)

Accepted Answer

$$y = y_0$ - \frac{1}{2} g t^2$

Question 16

If a vector $$\vec{B}$$ makes an angle $$	heta$$ with the x-axis, what is its y-component? (Chapter 3.4-3.5)

Accepted Answer

$$B_y = |\vec{B}| \sin 	heta$$

Question 17

A student walks 5 m east, then 12 m north. What is the direction of the displacement vector relative to east? (Chapter 3.4-3.5)

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{12}{5}ight) \approx 67.4^\circ$$ north of east

Question 18

Which operation results in a vector perpendicular to both $$\vec{A}$$ and $$\vec{B}$$? (Chapter 3.4-3.5)

Accepted Answer

$$\vec{A} 	imes \vec{B} ($$cross product)

Fundamental Concepts in Physics: Models, Motion, and Vectors

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