Final answer:
The y-component of a vector with a magnitude of 44.9 and a direction of 50.4 degrees is calculated using the sine function and is approximately 34.56, corresponding to option (B).
Step-by-step explanation:
The question pertains to determining the y-component of a vector with a given magnitude and direction angle. To find the y-component of a vector, we can use the sine function, since the y-component corresponds to the opposite side of the angle in a right triangle formed by the vector. Therefore, we calculate the y-component (Ay) as:
Ay = A sin(θ),
where A is the magnitude of the vector and θ is the direction angle. Plugging in the values given in the question:
Ay = 44.9 sin(50.4°).
Using a calculator, we get:
Ay ≈ 44.9 × 0.7716,
Ay ≈ 34.64.
Thus, the correct answer for the y-component of the vector is approximately 34.56, which corresponds to option (B).