Final answer:
The soccer ball lands 83.3 m away from the cliff when it is kicked horizontally at 29.0 m/s off of a 25.0 m cliff. This calculation is made by determining the time it takes for the ball to fall vertically and then using that to find the horizontal distance covered.
Step-by-step explanation:
The problem presented is a classic example of a projectile motion issue in physics. In this scenario, a soccer ball is kicked horizontally off a cliff, which means the vertical and horizontal motions can be analyzed independently. To calculate the horizontal distance the ball travelled before landing, we need to determine the time it takes to fall vertically 25.0 m, and then use this time to find out how far it went horizontally at a constant speed of 29.0 m/s.
First, let's find the time it takes for the ball to hit the ground. The equation for the distance covered in free fall is d = 1/2 * g * t^2, where g is acceleration due to gravity (9.8 m/s2). Rearranging the equation for time, we get t = sqrt(2 * d / g). Plugging in the values, we get t = sqrt(2 * 25.0 m / 9.8 m/s2), which gives us the time the ball takes to fall.
Next, we calculate the horizontal distance x using the formula x = velocity * time. With a horizontal velocity of 29.0 m/s and the time calculated in the first step, we can find the horizontal distance.
Using these calculations, we determine that the ball lands 83.3 m away from the point of kick, which corresponds to option A.