Question

A 3 kg ball rolls off a 33 m high cliff, and lands 23 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.)

Answer 1

F=<0,-29.4,0>N

D = <0,-10,0>m

Work=F·D=294 Joules

Step-by-step explanation:

Force:

The gravity has a negative direction in the axis Y in our coordinate system:

F=<0,-mg,0>=<0,-3*9.8,0>=<0,-29.4,0>N

Displacement:

The initial position A is <0, 33, 0>m

The final position B is <0, 23,0>m

The displacement vector is D=B-A = <0,-10,0>m

Gravitational Work:

The work is the scalar product between the force and the displacement

Work=F·D=(-29.4)*(-10)=294 Joules