Final answer:
The x-component of a velocity vector at 40° above the positive x-axis with a y-component of 10 m/s is calculated using trigonometric functions and is approximately 11.92 m/s.
Step-by-step explanation:
The student has asked for the x-component of a velocity vector that is 40° above the positive x-axis with a y-component of 10 m/s. To find the x-component of the vector, we can use trigonometric functions, specifically the cosine function, because it relates the adjacent side (x-component) to the hypotenuse in the context of the angle given. Using the formula:
x-component = hypotenuse × cos(angle), where the hypotenuse (v) can be determined from the y-component:
sin(angle) = y-component / hypotenuse ⇒ hypotenuse = y-component / sin(angle)
We need to find the hypotenuse first:
hypotenuse = 10 m/s / sin(40°) ≈ 10 m/s / 0.643 ≈ 15.55 m/s
Then, we can find the x-component:
x-component = 15.55 m/s × cos(40°) ≈ 15.55 m/s × 0.766 ≈ 11.92 m/s.
However, none of the choices A) 8.11 m/s, B) 6.08 m/s, C) 7.66 m/s, or D) 5.48 m/s match the calculated value, suggesting there may have been an error in the question options as provided. The calculated answer should be approximately 11.92 m/s.