Q: A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its maximum range $$R ($$assuming $$y_0 = 0$)?

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

Q: If a vector $$\vec{A}$$ has components $$A_x$$ and $$A_y$$, what is the direction $$\theta of$$ $$\vec{A}$$ relative to the $$x-$$axis?

$$\theta = \arctan\left(\dfrac{A_y}{A_x}\right)$$

Question 1

Which of the following physical quantities is a vector?

Accepted Answer

Displacement

Question 2

A car travels 8 km east and then 6 km west. What is the magnitude of its resultant displacement?

Accepted Answer

$$8 - 6 = 2\ \mathrm{km}$$

Question 3

If two vectors $$\vec{A}$$ and $$\vec{B}$$ are perpendicular, what is the magnitude of their sum $$\vec{R}$$?

Accepted Answer

$$\sqrt{|\vec{A}|^2 + |\vec{B}|^2}$$

Question 4

A vector $$\vec{V} is $$multiplied by a scalar $$c = -2. $$What is the result?

Accepted Answer

A vector with magnitude $$2|\vec{V}| in $$the opposite direction to $$\vec{V}$$

Question 5

Given a vector $$\vec{V}$$ with components $$V_x = 3$$ and $$V_y = 4$$, what is its magnitude?

Accepted Answer

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

Question 6

A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its maximum range $$R ($$assuming $$y_0 = 0$)?

Accepted Answer

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

Question 7

A rural mail carrier drives 22.0 km north, then 47.0 km at 60.0° south of east. What is the correct method to find her total displacement?

Accepted Answer

Resolve each leg into $$x$$ and $$y$$ components, sum components, then use $$D = \sqrt{D_x^2$ + D_y^2$}$$

Question 8

Which equation gives the $$y-$$position of a projectile as a function of time $$t$$, if $$y_0 is $$the initial height and $$v_{0y} is $$the initial vertical velocity?

Accepted Answer

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

Question 9

A ball is thrown horizontally from a cliff. Which statement is true about its motion?

Accepted Answer

Its horizontal velocity remains constant while its vertical velocity increases linearly with time

Question 10

Which of the following is the correct vector equation for instantaneous velocity in three dimensions using unit vectors?

Accepted Answer

$$\vec{v} = \dfrac{d\vec{r}}{dt} = \dfrac{dx}{dt} \hat{i} + \dfrac{dy}{dt} \hat{j} + \dfrac{dz}{dt} \hat{k}$$

Question 11

An airplane pilot wants to fly due east, but there is a wind blowing due north. Which direction should the pilot point the plane relative to the air?

Accepted Answer

South of east

Question 12

A boat can travel at $$1.85\ \mathrm{m/s} in $$still water. If the river current is $$1.20\ \mathrm{m/s}$$, what is the minimum time to cross a river $$100\ \mathrm{m}$$ wide?

Accepted Answer

$$t = \dfrac{100}{1.85}$$

Question 13

Which of the following is NOT a step in solving a projectile motion problem?

Accepted Answer

Add the $$x$$ and $$y$$ velocities together directly

Question 14

If a vector $$\vec{A}$$ has components $$A_x$$ and $$A_y$$, what is the direction $$	heta of$$ $$\vec{A}$$ relative to the $$x-$$axis?

Accepted Answer

$$	heta = \arctan\left(\dfrac{A_y}{A_x}ight)$$

Question 15

Which statement about projectile motion is correct?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity changes due to gravity

Question 16

A vector $$\vec{V} is $$written in terms of unit vectors as $$\vec{V} = V_x \hat{i} + V_y \hat{j} + V_z \hat{k}. $$What is the magnitude of $$\vec{V}$$?

Accepted Answer

$$\sqrt{V_x^2$ + V_y^2$ + V_z^2$}$$

Question 17

Which equation describes the parabolic trajectory of a projectile launched from the origin with initial velocities $$v_{x0}$$ and $$v_{y0}$$?

Accepted Answer

$$y = \left(\dfrac{v_{y0}}{v_{x0}}\right)x - \left(\dfrac{g}{2v_{x0}^2}\$$right)x^2$$

Question 18

A vector $$\vec{A} is $$subtracted from $$\vec{B}$$, i.e., $$\vec{B} - \vec{A}. $$Which graphical method correctly represents this operation?

Accepted Answer

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

Kinematics in Two or Three Dimensions and Vectors: Chapter 3 Study Notes

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