Final answer:
The vertical component of the velocity of the ball, when kicked with an initial velocity of 82 feet per second at an angle of 58°, is approximately 69.54 feet per second.
Step-by-step explanation:
This problem falls under the domain of Physics, specifically the sub-discipline of kinematics. To calculate the vertical component of the velocity of the ball, we use the formula V₀ * sin(ϴ), where V₀ is the initial velocity, ϴ is the angle, and sin is the trigonometric function sine.
In this case, the initial velocity (V₀) is 82 feet per second and the angle (ϴ) is 58°. Substituting these values into the formula gives us 82 * sin(58°). Using a calculator, we find that the vertical component of the velocity vector is approximately 69.54 feet per second. Therefore, the correct answer is option C: 69.54.
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