Final answer:
The horizontal component of the initial velocity is 33.2 m/s, the vertical component is 29.5 m/s, and the time the golf ball is in the air is 4.42 s. The closely related option is A) vx = 33.2 m/s, vy = 29.5 m/s, time = 4.27 s.
Step-by-step explanation:
To find the horizontal and vertical components of the initial velocity, we can use trigonometry. The horizontal component (vx) is given by vx = v * cos(angle), where v is the initial velocity and angle is the launch angle. In this case, vx = 44.6 m/s * cos(50.3°) = 33.2 m/s.
The vertical component (vy) is given by vy = v * sin(angle), where vy is the initial vertical velocity.
In this case, vy = 44.6 m/s * sin(50.3°) = 29.5 m/s.
The time the golf ball is in the air can be calculated using the vertical motion. Since the ball is projected vertically upwards and then falls, we can find the total time by dividing the time it takes for the ball to reach its highest point and the time it takes for the ball to fall back to the ground.
The time to reach the highest point is given by t = vy / g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, t = 29.5 m/s / 9.8 m/s^2
= 3.01 s.
The time to fall back to the ground is given by t = sqrt(2h / g), where h is the maximum height reached by the ball. In this case, the ball lands 20.0 m below its starting altitude, so the maximum height is 20.0 m.
Therefore, t = sqrt(2 * 20.0 m / 9.8 m/s^2) = 1.41 s.
The total time the golf ball is in the air is the sum of these two times, which is 3.01 s + 1.41 s = 4.42 s.