Exam 2 Vocabulary Exam

A vector is a quantity that has both magnitude and direction. It is represented by an arrow, where the direction of the arrow indicates the direction of the quantity and the length of the arrow is proportional to the magnitude of the quantity. Scalars, on the other hand, only have magnitude and do not have a specific direction associated with them. The Pythagorean Theorem is a mathematical formula used to calculate the length of the sides of a right triangle. The other options listed are not relevant to the given description.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is represented by the equation a^2 + b^2 = c^2, where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse. Therefore, the given equation a^2 + b^2 = c^2 represents the Pythagorean Theorem.

A scalar is a quantity that is fully described by a magnitude (or numerical value) alone. Unlike a vector, which has both magnitude and direction, a scalar only has magnitude. In this context, the term "scalar" refers to a quantity that does not have any associated direction, and can be represented by a single numerical value.

The hypotenuse is always the side opposite the right angle in a right triangle. It is also the longest side in a right triangle.

Theta is the correct answer because it represents an unknown/known angle measure. In mathematics and physics, theta is commonly used to denote an angle. It is a variable that can take on different values, representing the measure of an angle in a given context. Theta is often used in trigonometry to represent angles in right triangles, as well as in other areas of mathematics and science where angles are involved.

The term "component" refers to the individual parts or elements of a vector. In this context, the x and y components of a vector represent its horizontal and vertical parts respectively. These components are perpendicular to each other and can be used to describe the vector's overall direction and magnitude.

The answer "Acceleration y-direction" is correct because it refers to the vertical acceleration of an object. In physics, when an object is in motion, it can have acceleration in both the x-direction (horizontal) and the y-direction (vertical). Acceleration y-direction specifically represents the rate of change of velocity in the vertical direction. It is usually denoted as "ay" and can be positive (when the object is moving upwards) or negative (when the object is moving downwards). This answer is relevant in the context of analyzing the motion of projectiles or objects moving in a vertical plane.

The given correct answer is "Horizontal". In this context, "horizontal" refers to a direction that goes side-to-side, specifically in the x-direction. It is one of the components of a vector that describes the motion of an object. The horizontal component represents the motion of the object in the x-axis or side-to-side direction.

The cosine function is defined as the ratio of the side adjacent to an acute angle in a right-angled triangle to the hypotenuse. It represents the horizontal component of the angle.

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The term "vertical" refers to a direction that is perpendicular to the horizontal plane. In this context, it is used to describe a direction going up-and-down, which is commonly represented by the y-axis in mathematics and physics. The y-direction is often used to analyze vertical motion or displacement in a coordinate system.

The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the hypotenuse is called the sine function.

The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right triangle) to the adjacent side of the given angle is the tangent.

The side across from a given angle in a right triangle is called the opposite side. In a right triangle, the opposite side is the side that is not adjacent to the given angle and is opposite to the angle. It is called the opposite side because it is on the opposite side of the right angle from the given angle.

A projectile refers to an object that is influenced only by the downward force of gravity. When an object is launched into the air, it follows a curved path known as a projectile motion. During its flight, the only force acting on it is gravity, which causes it to accelerate downward. The object's horizontal motion remains unaffected by gravity, resulting in a parabolic trajectory. Therefore, a projectile is an object that experiences a vertical acceleration due to gravity while its horizontal motion remains constant.