Final answer:
The initial vertical component of the projectile's velocity is calculated using trigonometry, specifically by multiplying the initial speed by the sine of the angle of projection. The calculation yields an initial vertical velocity of approximately 32.14 m/s, which is not among the provided options.
Step-by-step explanation:
To find the initial vertical component of the projectile's velocity, we use the relationship in trigonometry that defines the vertical component of a velocity vector when given the magnitude of the velocity and the angle of projection. The formula is Vy = V * sin(θ) where Vy is the initial vertical velocity, V is the initial speed, and θ is the angle of projection.
Given the initial speed of 50.0 m/s and an angle of 40.0° to the horizon, we can calculate the initial vertical component of velocity as follows:
Vy = 50.0 m/s * sin(40.0°)
After calculating the sine of 40.0° which is approximately 0.6428, we multiply it by 50.0 m/s:
Vy = 50.0 m/s * 0.6428 = 32.14 m/s
Therefore, the initial vertical component of the velocity is closest to 32.14 m/s, which is not listed in the options given by the student.