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A 2 kg ball rolls off a 26 m high cliff, and lands 29 m from the base of the cliff. Express the displacement and the gravitational force in terms of vectors and calculate the work done by the gravitational force. Note that the gravitational force is < 0, -mg, 0 >, where g is a positive number (+9.8 N/kg). (Let the origin be at the base of the cliff, with the +x direction towards where the ball lands, and the +y direction taken to be upwards.)

User Jon Artus
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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).

User Michael Hallock
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