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Ch 03: Vectors and Coordinate Systems
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 38

A jet plane taking off from an aircraft carrier has acceleration a = ( 15 m/s², 22° above horizontal). What are the horizontal and vertical components of the jet's acceleration?

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Start by understanding that the acceleration vector is given in polar form with a magnitude of 15 m/s² and a direction of 22° above the horizontal. To find the horizontal and vertical components, we will use trigonometric functions.
The horizontal component of acceleration (aₓ) can be found using the cosine function: aₓ = a * cos(θ), where 'a' is the magnitude of the acceleration (15 m/s²) and 'θ' is the angle (22°).
The vertical component of acceleration (aᵧ) can be found using the sine function: aᵧ = a * sin(θ), where 'a' is the magnitude of the acceleration (15 m/s²) and 'θ' is the angle (22°).
Substitute the given values into the formulas: aₓ = 15 * cos(22°) and aᵧ = 15 * sin(22°).
Evaluate the trigonometric functions (cos(22°) and sin(22°)) to compute the horizontal and vertical components of the acceleration. These will give you the final values for aₓ and aᵧ.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Vector Components

Vectors can be broken down into their horizontal and vertical components using trigonometric functions. For a vector at an angle, the horizontal component is found using the cosine function, while the vertical component is determined using the sine function. This decomposition is essential for analyzing motion in two dimensions.
추천 영상:
가이드 코스
07:30
Vector Addition By Components

Trigonometric Functions

Trigonometric functions, specifically sine and cosine, relate the angles of a triangle to the ratios of its sides. In the context of vector components, cosine gives the adjacent side (horizontal component) and sine gives the opposite side (vertical component) when applied to the angle of the vector. Understanding these functions is crucial for resolving vectors.
추천 영상:
가이드 코스
08:30
Intro to Wave Functions

Acceleration

Acceleration is the rate of change of velocity of an object and is a vector quantity, meaning it has both magnitude and direction. In this scenario, the acceleration of the jet plane is given in terms of its magnitude and direction, which must be resolved into components to analyze its motion in the horizontal and vertical directions effectively.
추천 영상:
가이드 코스
05:47
Intro to Acceleration
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