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

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

Q: A vector $\vec{v}$ has components $v_x = -5$ and $v_y = 12$. What is the angle $\theta$ it makes with the positive $x$-axis?

$\theta = \tan^{-1}\left(\frac{12}{-5}\right)$

Q: Which of the following is true about the dot product of two vectors $\vec{a}$ and $\vec{b}$?

$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$

Question 1

A car travels 1200 meters in 3 minutes. What is its average speed in meters per second ($\frac{m}{s}$)?

Accepted Answer

$6.67\ \frac{m}{s}$

Question 2

Given a vector $\vec{v} = 3\hat{i} + 4\hat{j}$, what is its magnitude?

Accepted Answer

$5$

Question 3

If $\vec{a} = 2\hat{i} + 3\hat{j}$ and $\vec{b} = 4\hat{i} - \hat{j}$, what is the dot product $\vec{a} \cdot \vec{b}$?

Accepted Answer

$11$

Question 4

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

Accepted Answer

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

Question 5

Which of the following correctly expresses the displacement vector $\Delta \vec{r}$ between two points $\vec{r}_1$ and $\vec{r}_2$?

Accepted Answer

$\Delta \vec{r} = \vec{r}_2 - \vec{r}_1$

Question 6

A ball is thrown vertically upward with initial velocity $v_0$. What is its velocity after time $t$? (Assume upward is positive and acceleration due to gravity is $-g$.)

Accepted Answer

$v = v_0 - gt$

Question 7

A vector $\vec{v}$ has components $v_x = -5$ and $v_y = 12$. What is the angle $	heta$ it makes with the positive $x$-axis?

Accepted Answer

$	heta = 	an^{-1}\left(\frac{12}{-5}ight)$

Question 8

Which of the following statements about the projection of a vector onto an axis is correct?

Accepted Answer

The projection equals the magnitude of the vector times the cosine of the angle between the vector and the axis.

Question 9

A projectile is fired horizontally from a cliff of height $h$ with initial speed $v_0$. How long does it take to hit the ground?

Accepted Answer

$t = \sqrt{\frac{2h}{g}}$

Question 10

If a vector $\vec{A}$ has components $A_x = 0$ and $A_y = 0$, what can be said about its direction?

Accepted Answer

The direction is undefined.

Question 11

A ball collides elastically with a vertical wall at $x = x_k$. Which component of its velocity changes sign after the collision?

Accepted Answer

The $x$-component

Question 12

Which formula gives the position $x$ of a particle moving with constant acceleration $a$ after time $t$, starting from $x_0$ with initial velocity $v_0$?

Accepted Answer

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

Question 13

A vector $\vec{v}$ is specified by its Cartesian components $v_x$ and $v_y$. What is the formula for its magnitude?

Accepted Answer

$|\vec{v}| = \sqrt{v_x^2 + v_y^2}$

Question 14

A projectile passes through the point $(x_0, y_0)$. Which condition must be satisfied at that instant?

Accepted Answer

$x = x_0,\ y = y_0$

Question 15

Which equation describes the velocity of a particle as the derivative of its position vector with respect to time?

Accepted Answer

$\vec{v} = \frac{d\vec{r}}{dt}$

Question 16

A vector $\vec{A}$ is projected onto the $y$-axis. If the angle between $\vec{A}$ and the $y$-axis is $	heta$, what is the projection?

Accepted Answer

$|\vec{A}| \cos 	heta$

Question 17

Which of the following is true about the dot product of two vectors $\vec{a}$ and $\vec{b}$?

Accepted Answer

$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$

Question 18

A ball collides with a horizontal surface at $y = y_k$. Which component of its velocity changes sign after the collision?

Accepted Answer

The $y$-component

Question 19

If a vector is measured with respect to the negative direction along an axis, what must be done to its projection?

Accepted Answer

A negative sign must be included in front of the projection.

Fundamental Concepts in Physics: Unit Conversions, Vectors, and Kinematics

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