On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. Find the horizontal and vertical components of the shell's initial velocity.

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Start by identifying the initial velocity of the shell, which is given as 40.0 m/s, and the angle of projection, which is 60.0° above the horizontal.

To find the horizontal component of the initial velocity, use the formula:

v

_x=vcosθ. Here,

v

is the initial velocity and

θ

is the angle of projection.

Substitute the given values into the formula for the horizontal component:

v

_x=40.0cos60.0°.

To find the vertical component of the initial velocity, use the formula:

v

_y=vsinθ. Again,

v

is the initial velocity and

θ

is the angle of projection.

Substitute the given values into the formula for the vertical component:

v

_y=40.0sin60.0°.

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주요 개념

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

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. It involves two components of motion: horizontal and vertical. Understanding projectile motion is crucial for analyzing the trajectory and velocity components of the shell in the given problem.

Vector Decomposition

Vector decomposition is the process of breaking down a vector into its horizontal and vertical components. In this problem, the initial velocity vector of the shell is decomposed using trigonometric functions, where the horizontal component is found using cosine and the vertical component using sine of the given angle.

Trigonometric Functions

Trigonometric functions, such as sine and cosine, are used to relate the angles and sides of a right triangle. In physics, they are essential for resolving vectors into components. For a vector with magnitude V at an angle θ, the horizontal component is V*cos(θ) and the vertical component is V*sin(θ), which are used to find the shell's velocity components.