Q: If a vector $$\vec{A}$$ has components $$A_x = 6$$ and $$A_y = 8$$, what is the direction angle $$\theta ($$measured from the $$x-$$axis) of $$\vec{A}$$?

$$\theta = \arctan\left(\frac{8}{6}\right) \approx 53.1^\circ$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which formula gives the horizontal range $$R ($$assuming it lands at the same height it was launched)?

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

Question 1

Which of the following statements correctly distinguishes between a scalar and a vector quantity?

Accepted Answer

A scalar has only magnitude, while a vector has both magnitude and direction.

Question 2

Given two vectors $$\vec{A}$$ and $$\vec{B}$$ with components $$\vec{A} = (3, 4)$$ and $$\vec{B} = (1, 2)$$, what is the magnitude of the resultant vector $$\vec{R} = \vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{53}$$

Question 3

A rock is thrown straight up from the roof of a 100 m tall building with an initial velocity of $$10\ \mathrm{m/s}. $$Ignoring air resistance, what is the maximum height above the ground the rock will reach? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$105.1\ \mathrm{m}$$

Question 4

Which equation correctly gives the $$x-$$component of a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the $$x-$$axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 5

A car travels 4 km east, then 3 km north. What is the magnitude of its net displacement?

Accepted Answer

$$5\ \mathrm{km}$$

Question 6

If a vector $$\vec{A}$$ has components $$A_x = 6$$ and $$A_y = 8$$, what is the direction angle $$	heta ($$measured from the $$x-$$axis) of $$\vec{A}$$?

Accepted Answer

$$	heta = \arctan\left(\frac{8}{6}ight) \approx 53.1^\circ$$

Question 7

A projectile is launched horizontally from a 20 m high cliff. How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 8

Which of the following best describes the difference between displacement and distance?

Accepted Answer

Displacement is the straight-line change in position (vector), distance is the total path length (scalar).

Question 9

A ball is thrown with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$20 \sin 30^\circ$$

Question 10

Which of the following equations gives the vertical position $$y of an $$object in free fall (starting from $$y_0) $$after time $$t$$, with initial vertical velocity $$v_{0y}$$ and acceleration $$g$$ downward?

Accepted Answer

$$y = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 11

A vector $$\vec{R}$$ has components $$R_x = -5$$ and $$R_y = 12. $$What is the magnitude of $$\vec{R}$$?

Accepted Answer

$$13$$

Question 12

If the $$x-$$component of a vector is negative and the $$y-$$component is positive, in which quadrant does the vector lie?

Accepted Answer

Second quadrant

Question 13

A person walks 3 km north, then 4 km east, then 3 km south. What is the magnitude of their net displacement?

Accepted Answer

$$4\ \mathrm{km}$$

Question 14

Which of the following is the correct formula for the average velocity $$\vec{v}_{avg}$$ over a time interval $$\Delta t$$?

Accepted Answer

$$\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}$$

Question 15

A stone is dropped from rest from a height $$h. $$What is its velocity just before hitting the ground? (Neglect air resistance, $$g is $$acceleration due to gravity)

Accepted Answer

$$v = \sqrt{2gh}$$

Question 16

Which of the following best describes the process of resolving a vector into its components?

Accepted Answer

Breaking a vector into two or more vectors that add up to the original vector, usually along perpendicular axes.

Question 17

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which formula gives the horizontal range $$R ($$assuming it lands at the same height it was launched)?

Accepted Answer

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

Question 18

If a vector $$\vec{A}$$ has a magnitude of $$10$$ and makes an angle of $$60^\circ$$ with the $$x-$$axis, what is its $$y-$$component?

Accepted Answer

$$10 \sin 60^\circ$$

Question 19

A ball is thrown horizontally from a 45 m high building with a speed of $$5\ \mathrm{m/s}. $$How far from the base of the building does the ball land? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$15.2\ \mathrm{m}$$

Vectors, Kinematics, and Free-Fall Motion: Physics Study Notes

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