Q: A projectile is launched from the ground with initial velocity $$v_0 at $$angle $$\theta$$ above the horizontal. Which equation gives the time to reach maximum height?

$$t = \frac{v_0$ \sin \theta}{g}$$

Q: A person walks 5 km north, then 12 km east. What is the direction of the net displacement from the starting point, measured east of north?

$$\tan$$^{-1}$$\left(\frac{12}{5}\right) = 67.38^\circ$$ east of north

Q: A soccer ball is kicked from the ground at $$20\ \mathrm{m/s}$$ and $$50^\circ$$ above the horizontal. If the ball lands at the same height, what is the total time of flight? (Use $$g = 10\ \mathrm{m/s}^2)$$

$$t = \frac{2 v_0$ \sin \theta}{g} = \frac{2 \times 20 \times \sin 50^\circ}{10} = 3.14\ \mathrm{s}$$

Question 1

A hiker walks 8 km east, then 6 km north. What is the magnitude of the hiker's net displacement from the starting point?

Accepted Answer

$$\sqrt{8^2$ + 6^2$} = 10 km$$

Question 2

Which of the following statements about vector addition is TRUE?

Accepted Answer

The order of vector addition does not affect the resultant vector.

Question 3

A soccer ball is kicked with an initial speed of $$20\ \mathrm{m/s} at an $$angle of $$50^\circ$$ above the horizontal. What is the initial vertical component of the velocity?

Accepted Answer

$$20 \sin 50^\circ = 15.32\ \mathrm{m/s}$$

Question 4

Which graphical method is used to add two vectors by placing them tail-to-tail and drawing a parallelogram?

Accepted Answer

Parallelogram method

Question 5

A boat moves with velocity $$\vec{v}_{bw}$$ relative to water, and the water flows with velocity $$\vec{v}_{ws}$$ relative to shore. What is the velocity of the boat relative to shore?

Accepted Answer

$$\vec{v}_{bs} = \vec{v}_{bw} + \vec{v}_{ws}$$

Question 6

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

Accepted Answer

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

Question 7

A projectile is launched from the ground with initial velocity $$v_0 at $$angle $$	heta$$ above the horizontal. Which equation gives the time to reach maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin 	heta}{g}$$

Question 8

Which of the following is NOT a property of vectors?

Accepted Answer

Vectors can be described by a single number.

Question 9

A person walks 5 km north, then 12 km east. What is the direction of the net displacement from the starting point, measured east of north?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{12}{5}ight) = 67.38^\circ$$ east of north

Question 10

Which of the following best describes the difference between scalars and vectors?

Accepted Answer

Scalars have magnitude only, while vectors have both magnitude and direction.

Question 11

A vector $$\vec{V} is $$multiplied by a negative scalar $$-2. $$What happens to the vector?

Accepted Answer

Its magnitude doubles and its direction reverses.

Question 12

A soccer ball is kicked from the ground at $$20\ \mathrm{m/s}$$ and $$50^\circ$$ above the horizontal. If the ball lands at the same height, what is the total time of flight? (Use $$g = 10\ \mathrm{m/s}^2)$$

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g} = \frac{2 	imes 20 	imes \sin 50^\circ}{10} = 3.14\ \mathrm{s}$$

Question 13

Which of the following is a correct statement about the component method for vector addition?

Accepted Answer

Each vector is broken into its $$x$$ and $$y$$ components, which are then summed separately.

Question 14

A train moves east at $$30\ \mathrm{m/s}$$, and a passenger walks north at $$5\ \mathrm{m/s}$$ relative to the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$$\sqrt{30^2$ + 5^2$} = 30.41\ \mathrm{m/s} at$$ $$	an$$^{-1}$$(5/30) = 9.46^\circ$$ north of east

Question 15

Which of the following is a real-world example of a vector quantity?

Accepted Answer

Wind velocity reported as 15 km/h at 30° north of east

Question 16

A vector $$\vec{A}$$ has magnitude $$A$$ and points at angle $$	heta$$ above the $$x-$$axis. What are its $$x$$ and $$y$$ components?

Accepted Answer

$$A_x = A \cos 	heta$$, $$A_y = A \sin 	heta$$

Question 17

Which of the following is NOT a valid method for adding vectors?

Accepted Answer

Multiplying their magnitudes

Question 18

A projectile is launched horizontally from a cliff. Which statement is correct about its motion?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases due to gravity.

Question 19

A vector $$\vec{B} is $$subtracted from vector $$\vec{A}$$ ($$\vec{A} - \vec{B}). $$Which graphical operation represents this?

Accepted Answer

Add $$\vec{A} to $$the negative of $$\vec{B}$$

Chapter 3 - Kinematics and Vectors in Two Dimensions (2D): Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard