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

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

Q: A vector $$ \vec{B} $$ has components $$ B_x = 6 $$ and $$ B_y = 8 . $$What is the direction of $$ \vec{B} $$ relative to the x-axis?

$$\theta = \tan$$^{-1}$$\left(\frac{8}{6}\right)$$

Q: A car drives up a slope at a constant speed of 15 m/s for 10 s. If the slope makes an angle $$ \theta = 10^\circ $$ with the horizontal, what is the height gained by the car?

$$h = 15 \times 10 \times \sin(10^\circ)$$

Q: A dog runs horizontally off a dock at 8.5 m/s from a height of 0.61 m. How long is the dog in the air before hitting the water?

$$t = \sqrt{\frac{2 \times 0.61}{9.8}}$$

Q: For a projectile launched at speed $$ v_0 $$ and angle $$ \theta $$ above the horizontal, what is the horizontal range (neglecting air resistance)?

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

Q: A speed skater covers 500 m in 45 s. What is her average speed?

$$\frac{500}{45} \approx 11.1\ \text{m/s}$$

Q: A car turns a corner with a radius of 25 m. If the maximum advisable acceleration is $$0.40g$$, what is the maximum speed?

$$v_{max} = \sqrt{0.40g \times 25}$$

Question 1

Which of the following statements best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

If a vector $$ \vec{A}  is $$multiplied by a negative scalar $$ -k $$, what happens to the resulting vector?

Accepted Answer

Its magnitude is multiplied by $$ k $$ and its direction is reversed.

Question 3

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

Accepted Answer

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

Question 4

Which method is NOT used for vector addition?

Accepted Answer

Scalar multiplication

Question 5

A vector $$ \vec{B} $$ has components $$ B_x = 6 $$ and $$ B_y = 8 . $$What is the direction of $$ \vec{B} $$ relative to the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{8}{6}ight)$$

Question 6

A car drives up a slope at a constant speed of 15 m/s for 10 s. If the slope makes an angle $$ 	heta = 10^\circ $$ with the horizontal, what is the height gained by the car?

Accepted Answer

$$h = 15 	imes 10 	imes \sin(10^\circ)$$

Question 7

A crate slides down a frictionless ramp tilted at angle $$ 	heta . $$What is the acceleration parallel to the ramp?

Accepted Answer

$$a = g \sin 	heta$$

Question 8

In projectile motion, which statement is correct regarding the horizontal and vertical components?

Accepted Answer

The vertical component has constant acceleration, and the horizontal component has zero acceleration.

Question 9

A dog runs horizontally off a dock at 8.5 m/s from a height of 0.61 m. How long is the dog in the air before hitting the water?

Accepted Answer

$$t = \sqrt{\frac{2 	imes 0.61}{9.8}}$$

Question 10

For a projectile launched at speed $$ v_0 $$ and angle $$ 	heta $$ above the horizontal, what is the horizontal range (neglecting air resistance)?

Accepted Answer

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

Question 11

A toy car moves around a circular track at constant speed. If its speed doubles, by what factor does its centripetal acceleration change?

Accepted Answer

It increases by a factor of 4.

Question 12

What is the formula for centripetal acceleration for an object moving in a circle of radius $$ r  at $$speed $$ v $$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 13

A speed skater covers 500 m in 45 s. What is her average speed?

Accepted Answer

$$\frac{500}{45} \approx 11.1\ 	ext{m/s}$$

Question 14

A car turns a corner with a radius of 25 m. If the maximum advisable acceleration is $$0.40g$$, what is the maximum speed?

Accepted Answer

$$v_{max} = \sqrt{0.40g 	imes 25}$$

Question 15

Which of the following is NOT a property of the zero vector?

Accepted Answer

It has a negative magnitude.

Question 16

If a projectile is launched horizontally from a height, what is its initial vertical velocity?

Accepted Answer

Zero

Question 17

When decomposing a vector into components, which trigonometric function is used to find the x-component if the angle is measured from the x-axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 18

A particle changes direction with no change in speed. What can be said about its acceleration?

Accepted Answer

It has nonzero acceleration due to change in direction.

Question 19

Which statement about vector subtraction is correct?

Accepted Answer

To subtract $$ \vec{B} $$ from $$ \vec{A} $$, reverse $$ \vec{B} $$ and add it to $$ \vec{A} .$$

Question 20

If a vector $$ \vec{A}  is $$rotated by an angle $$ \phi $$, how do its components change?

Accepted Answer

The components are recalculated using the new axes: $$A'_x = A \cos(	heta - \phi)$$, $$A'_y = A \sin(	heta - \phi)$$

Chapter 3: Vectors and Motion in Two Dimensions - Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드