Final answer:
Using kinematics, the ball takes approximately 4 seconds to hit the ground, and the total distance it falls is approximately 272.4 feet, which is not among the options provided.
Step-by-step explanation:
The question involves calculating the time it takes for a golf ball to fall to the ground and how far it will fall. We can solve this problem using the principles of kinematics in two dimensions. Since the golf ball is hit at an upward angle, we will find the vertical component of the initial velocity and use it to calculate the time the ball takes to reach its maximum height, and then the time it takes to fall down to the ground from there.
First, we calculate the vertical component of the initial velocity (Vy = V * sin(θ)), which is 128 ft/s * sin(30°) = 64 ft/s. Next, we use the kinematic equation to find the time it takes to reach the peak: 0 = Vy - g*t, which simplifies to t = Vy/g. Plugging in the numbers, we get t = 64 ft/s / 32.2 ft/s² ≈ 2 seconds to reach the peak.
Since the time to go up and come down is the same, it will also take 2 seconds to fall down from the peak. Adding the time it takes to fall the extra 80 feet (from the height of the hill), we use the equation d = 0.5 * g * t² to find the time for this part. Solving for t gives us approximately 2 seconds. So the total time for the ball to hit the ground is roughly 4 seconds.
To find the distance the ball falls, we use the equation d = Vy * t + 0.5 * g * t². Since we calculated the time for the fall to be 2 seconds from the peak to the ground level, the equation simplifies to d = 64 ft/s * 2 s + 0.5 * (32.2 ft/s²) * (2 s)² = 128 ft + 64.4 ft ≈ 192.4 ft. However, we must also add the height of the hill to get the total distance fallen, which gives us approximately 272.4 feet.
Thus, the correct answer is none of the options provided. The ball takes roughly 4 seconds to hit the ground, and the total distance it falls is approximately 272.4 feet, not just 256 feet or 64 feet as listed in the options.