A soccer player kicks a ball with an initial velocity of 10...

A soccer player kicks a ball with an initial velocity of 10 . meters per second at an angle of $30 .{ }^{\circ}$ above the horizontal. The magnitude of the horizontal component of the ball's initial velocity is (A) $5.0 \mathrm{~m} / \mathrm{s}$ (B) $8.7 \mathrm{~m} / \mathrm{s}$ (C) $9.8 \mathrm{~m} / \mathrm{s}$ (D) $10 . \mathrm{m} / \mathrm{s}$

A soccer player kicks a ball with an initial velocity of 10 . meters per second at an angle of $30 .{ }^{\circ}$ above the horizontal. The magnitude of the horizontal component of the ball's initial velocity is
(A) $5.0 \mathrm{~m} / \mathrm{s}$
(B) $8.7 \mathrm{~m} / \mathrm{s}$
(C) $9.8 \mathrm{~m} / \mathrm{s}$
(D) $10 . \mathrm{m} / \mathrm{s}$

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Key Concepts

Projectile Motion

Projectile motion refers to the movement of an object that is launched into the air and then moves under the influence of gravity. It involves analyzing the object's motion in both horizontal and vertical directions, where the horizontal motion is constant (absent air resistance) and the vertical motion is affected by gravitational acceleration.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its horizontal and vertical components. In the context of projectile motion, this technique allows for separate analysis of the components of the initial velocity, making it easier to determine factors such as range, maximum height, and time of flight.

Trigonometric Functions

Trigonometric functions, such as cosine and sine, are used to relate angles to side lengths in right triangles. In projectile motion problems, the cosine function specifically helps to calculate the horizontal component of the initial velocity when the magnitude of the velocity and the angle of projection are known.

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