The height of the cliff is found by analyzing the vertical component of projectile motion. Using the time of flight (5 seconds) calculated from the given horizontal range and speed, and the formula for vertical displacement due to gravity, the height rounds to the nearest provided option, 150 meters.
The question involves calculating the height of a cliff from which a cannonball is launched horizontally. To solve this, we'll use the physics of projectile motion, specifically, the equations of motion under uniform acceleration due to gravity.
While the horizontal velocity is constant (50 m/s), the vertical motion can be analyzed independently. The vertical motion of the cannonball is only affected by gravity (9.81 m/s2). We are given the horizontal range (250 m) and the horizontal velocity (50 m/s), which allows us to calculate the time of flight:
Time = Horizontal Range / Horizontal Velocity = 250 m / 50 m/s = 5 seconds
Now, using the formula for vertical displacement (s = ut + (1/2)at2, where u is initial velocity, a is acceleration, and t is time), and knowing that the initial vertical velocity (u) is 0 m/s for horizontal launch, we find the height (s) of the cliff:
s = 0 m/s × 5 s + (1/2) × 9.81 m/s2 × (5s)2 = (1/2) × 9.81 m/s2 × 25 = 122.625 meters
However, since 122.625 meters is not an option in the provided choices, we must round it to the closest option given, which is Option C: 150 meters.