Final answer:
The displacement of the ball is 29 m in the +x direction. The gravitational force is represented as <0, -mg, 0 >. The work done by the gravitational force can be calculated as -mg * |d| * cos(0).
Step-by-step explanation:
The displacement of the ball can be calculated by finding the difference between the initial and final positions of the ball. In this case, the ball starts at a height of 26 m and lands 29 m from the base of the cliff, so the displacement is equal to the final position (29 m) minus the initial position (0 m), resulting in a displacement of 29 m in the +x direction.
The gravitational force can be represented as a vector in terms of magnitude and direction. In this case, the gravitational force is given as < 0, -mg, 0 >, where g is a positive number (+9.8 N/kg). The x-component of the gravitational force is 0, the y-component is -mg (-19.6 N), and the z-component is also 0.
To calculate the work done by the gravitational force, we can use the formula W = F · d, where W is the work, F is the force, and d is the displacement. Since the gravitational force points in the same direction as the displacement, the angle between the force and displacement vectors is 0 degrees. Therefore, the work done by the gravitational force can be calculated as W = F · d = |F| * |d| * cos(0) = -mg * |d| * cos(0).