To find the time of flight and the distance from the base of the cliff to the point where the ball lands, we can use the equations of motion.
First, let's determine the time of flight. Since the ball is thrown horizontally, it only experiences motion in the vertical direction due to gravity. The vertical motion can be described using the equation:
h = ut + (1/2)gt^2
Where:
h = height (256 ft)
u = initial vertical velocity (0 ft/s since the ball is thrown horizontally)
g = acceleration due to gravity (32.2 ft/s^2)
t = time of flight
Substituting the given values into the equation, we have:
256 = 0*t + (1/2)*32.2*t^2
256 = 16.1*t^2
Dividing both sides by 16.1, we get:
t^2 = 15.79
Taking the square root of both sides, we find:
t ≈ 3.97 seconds
Therefore, the time of flight of the ball is approximately 3.97 seconds.
Next, let's calculate the horizontal distance traveled by the ball. Since the initial horizontal velocity is constant throughout the motion, we can use the equation:
d = ut
Where:
d = horizontal distance
u = initial horizontal velocity (50 ft/s)
t = time of flight (3.97 seconds)
Substituting the given values into the equation, we have:
d = 50 * 3.97
d ≈ 198.5 feet
Therefore, the distance from the base of the cliff to the point where the ball lands is approximately 198.5 feet.