A 5 kg ball rolls off a 29 m high cliff, and lands 27 m from the base of the cli

Question

A 5 kg ball rolls off a 29 m high cliff, and lands 27 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.)

Displacement vector r = < ??,??,??> m

Gravitational Force vector F = < ??,??,??> N

Work W = ???? J

Explanation / Answer

displacement: < 27, -29, 0 >
The vertical displacement = 29 m
Force: < 0, -5(9.8), 0 >
The gravitation force = mg = (5)(9.8) = 49 N
W = Fd = <0, -49, 0 ><27, -29, 0 >
W = -49(-29) = 1421 J

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