Final answer:
To determine the horizontal displacement of the cannonball, you can use the equation x = v*t, where x is the horizontal displacement, v is the initial horizontal velocity, and t is the time. From the given information, the initial horizontal velocity is 42.5 m/s and the time is 6.9 s. Plugging in these values, the horizontal displacement is 293.25 m.
Step-by-step explanation:
To determine the horizontal displacement of the cannonball, we need to consider its initial horizontal velocity and the time it takes to reach the ground. Since the cannonball is launched horizontally, its initial horizontal velocity is the same as its original speed, which is 42.5 m/s. We can use the equation x = v*t, where x is the horizontal displacement, v is the initial horizontal velocity, and t is the time.
First, we need to find the time it takes for the cannonball to reach the ground. We can use the equation y = (1/2)gt^2, where y is the vertical displacement (which is equal to the height of the cliff, 154 m), and g is the acceleration due to gravity (-9.8 m/s^2).
Solving for t, we have 154 = (1/2)(-9.8)t^2, which gives us t = sqrt(154/4.9) = 6.9 s.
Now, we can use x = v*t = 42.5 * 6.9 = 293.25 m.