Vectors and Motion in Two Dimensions - AP Physics 1
Card 1 of 30
What is the two-dimensional motion with constant acceleration called?
What is the two-dimensional motion with constant acceleration called?
Tap to reveal answer
Projectile motion. Motion under gravity in two dimensions.
Projectile motion. Motion under gravity in two dimensions.
← Didn't Know|Knew It →
What does the magnitude of the cross product represent?
What does the magnitude of the cross product represent?
Tap to reveal answer
Area of the parallelogram formed. Geometric interpretation of cross product.
Area of the parallelogram formed. Geometric interpretation of cross product.
← Didn't Know|Knew It →
What is the direction of centripetal force in circular motion?
What is the direction of centripetal force in circular motion?
Tap to reveal answer
Toward the center of the circle. Keeps object in circular path.
Toward the center of the circle. Keeps object in circular path.
← Didn't Know|Knew It →
What is the effect of air resistance on projectile motion?
What is the effect of air resistance on projectile motion?
Tap to reveal answer
It decreases range and height. Air drag opposes motion.
It decreases range and height. Air drag opposes motion.
← Didn't Know|Knew It →
Identify the velocity of a projectile at its highest point.
Identify the velocity of a projectile at its highest point.
Tap to reveal answer
Zero vertical velocity. Instantaneously stops rising.
Zero vertical velocity. Instantaneously stops rising.
← Didn't Know|Knew It →
What is the formula for the gravitational potential energy of an object?
What is the formula for the gravitational potential energy of an object?
Tap to reveal answer
$U = mgh$. Height-dependent gravitational energy.
$U = mgh$. Height-dependent gravitational energy.
← Didn't Know|Knew It →
Which factor remains constant in a projectile's horizontal motion?
Which factor remains constant in a projectile's horizontal motion?
Tap to reveal answer
Horizontal velocity. No horizontal acceleration exists.
Horizontal velocity. No horizontal acceleration exists.
← Didn't Know|Knew It →
Find the vector sum of $(1, 2, 3)$ and $(4, 5, 6)$.
Find the vector sum of $(1, 2, 3)$ and $(4, 5, 6)$.
Tap to reveal answer
$(5, 7, 9)$. Add components: $(1+4, 2+5, 3+6)$.
$(5, 7, 9)$. Add components: $(1+4, 2+5, 3+6)$.
← Didn't Know|Knew It →
What is the relationship between period and frequency?
What is the relationship between period and frequency?
Tap to reveal answer
$T = \frac{1}{f}$. Period and frequency are reciprocals.
$T = \frac{1}{f}$. Period and frequency are reciprocals.
← Didn't Know|Knew It →
State the formula for angular displacement.
State the formula for angular displacement.
Tap to reveal answer
$\theta = \omega t$. Angle equals rate times time.
$\theta = \omega t$. Angle equals rate times time.
← Didn't Know|Knew It →
Define the term 'scalar quantity'.
Define the term 'scalar quantity'.
Tap to reveal answer
A quantity with magnitude only. No directional information included.
A quantity with magnitude only. No directional information included.
← Didn't Know|Knew It →
State the formula for the dot product of vectors $(a_1, b_1)$ and $(a_2, b_2)$.
State the formula for the dot product of vectors $(a_1, b_1)$ and $(a_2, b_2)$.
Tap to reveal answer
$a_1 a_2 + b_1 b_2$. Multiply corresponding components and sum.
$a_1 a_2 + b_1 b_2$. Multiply corresponding components and sum.
← Didn't Know|Knew It →
State the component form of vector $\textbf{A}$ with magnitude $5$ at $30^{\circ}$.
State the component form of vector $\textbf{A}$ with magnitude $5$ at $30^{\circ}$.
Tap to reveal answer
$(4.33, 2.5)$. Use $x = 5\cos(30°)$, $y = 5\sin(30°)$.
$(4.33, 2.5)$. Use $x = 5\cos(30°)$, $y = 5\sin(30°)$.
← Didn't Know|Knew It →
Identify the vertical component of velocity for a projectile at launch speed $v$ and angle $\theta$.
Identify the vertical component of velocity for a projectile at launch speed $v$ and angle $\theta$.
Tap to reveal answer
$v \sin \theta$. Initial vertical velocity component.
$v \sin \theta$. Initial vertical velocity component.
← Didn't Know|Knew It →
What is the range formula for a projectile launched at $v$ and angle $\theta$?
What is the range formula for a projectile launched at $v$ and angle $\theta$?
Tap to reveal answer
$R = \frac{v^2 \sin 2\theta}{g}$. Uses $\sin(2\theta)$ identity.
$R = \frac{v^2 \sin 2\theta}{g}$. Uses $\sin(2\theta)$ identity.
← Didn't Know|Knew It →
What is the horizontal component of velocity for a projectile at launch speed $v$ and angle $\theta$?
What is the horizontal component of velocity for a projectile at launch speed $v$ and angle $\theta$?
Tap to reveal answer
$v \cos \theta$. Horizontal component stays constant.
$v \cos \theta$. Horizontal component stays constant.
← Didn't Know|Knew It →
Which operation combines two vectors to form a resultant vector?
Which operation combines two vectors to form a resultant vector?
Tap to reveal answer
Vector addition. Forms resultant from two vectors.
Vector addition. Forms resultant from two vectors.
← Didn't Know|Knew It →
What is the resultant vector of $(3, 4)$ and $(1, 2)$?
What is the resultant vector of $(3, 4)$ and $(1, 2)$?
Tap to reveal answer
$(4, 6)$. Add corresponding components.
$(4, 6)$. Add corresponding components.
← Didn't Know|Knew It →
What is the formula for the velocity of an object in circular motion?
What is the formula for the velocity of an object in circular motion?
Tap to reveal answer
$v = r \omega$. Links linear and angular motion.
$v = r \omega$. Links linear and angular motion.
← Didn't Know|Knew It →
What condition indicates two vectors are perpendicular?
What condition indicates two vectors are perpendicular?
Tap to reveal answer
Dot product equals zero. Orthogonal vectors have zero dot product.
Dot product equals zero. Orthogonal vectors have zero dot product.
← Didn't Know|Knew It →
What variable represents angular velocity?
What variable represents angular velocity?
Tap to reveal answer
$\omega$. Greek omega represents rotation rate.
$\omega$. Greek omega represents rotation rate.
← Didn't Know|Knew It →
What is the definition of a vector quantity?
What is the definition of a vector quantity?
Tap to reveal answer
A quantity with both magnitude and direction. Combines size and direction info.
A quantity with both magnitude and direction. Combines size and direction info.
← Didn't Know|Knew It →
What is the dot product of vectors $(2, 3)$ and $(4, -1)$?
What is the dot product of vectors $(2, 3)$ and $(4, -1)$?
Tap to reveal answer
$5$. $(2)(4) + (3)(-1) = 8 - 3 = 5$.
$5$. $(2)(4) + (3)(-1) = 8 - 3 = 5$.
← Didn't Know|Knew It →
State the relationship between linear speed and angular speed.
State the relationship between linear speed and angular speed.
Tap to reveal answer
$v = r \omega$. Fundamental circular motion relationship.
$v = r \omega$. Fundamental circular motion relationship.
← Didn't Know|Knew It →
What is the projection of vector $\textbf{A}$ onto vector $\textbf{B}$?
What is the projection of vector $\textbf{A}$ onto vector $\textbf{B}$?
Tap to reveal answer
$\frac{\textbf{A} \cdot \textbf{B}}{||\textbf{B}||}$. Component of A along B direction.
$\frac{\textbf{A} \cdot \textbf{B}}{||\textbf{B}||}$. Component of A along B direction.
← Didn't Know|Knew It →
What is the formula for work done by a force in the direction of displacement?
What is the formula for work done by a force in the direction of displacement?
Tap to reveal answer
$W = Fd \cos \theta$. Force component in displacement direction.
$W = Fd \cos \theta$. Force component in displacement direction.
← Didn't Know|Knew It →
State the formula for the maximum height of a projectile.
State the formula for the maximum height of a projectile.
Tap to reveal answer
$h = \frac{v^2 \sin^2 \theta}{2g}$. From energy or kinematics.
$h = \frac{v^2 \sin^2 \theta}{2g}$. From energy or kinematics.
← Didn't Know|Knew It →
What is the cross product of vectors used to find?
What is the cross product of vectors used to find?
Tap to reveal answer
Vector perpendicular to both vectors. Cross product creates perpendicular vector.
Vector perpendicular to both vectors. Cross product creates perpendicular vector.
← Didn't Know|Knew It →
What is the angle between vectors $(1, 0)$ and $(0, 1)$?
What is the angle between vectors $(1, 0)$ and $(0, 1)$?
Tap to reveal answer
$90^{\circ}$. Unit vectors along axes are perpendicular.
$90^{\circ}$. Unit vectors along axes are perpendicular.
← Didn't Know|Knew It →
State the formula for the magnitude of a vector $(x, y)$.
State the formula for the magnitude of a vector $(x, y)$.
Tap to reveal answer
$\text{Magnitude} = \sqrt{x^2 + y^2}$. Pythagorean theorem for vector length.
$\text{Magnitude} = \sqrt{x^2 + y^2}$. Pythagorean theorem for vector length.
← Didn't Know|Knew It →