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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.)

Respuesta :

Answer:

Explanation:

mass of ball, m = 2 kg

height along negative Y axis, h = 26 m

distance along positive X axis, d = 29 m

Displacement in vector form is

[tex]\overrightarrow{d} = 29\widehat{i}-26\widehat{j}[/tex]

Gravitational force, mg downwards

[tex]\overrightarrow{F} = -mg\widehat{j}[/tex]

Work done by the gravitational force

[tex]W = \overrightarrow{F}.\overrightarrow{d}[/tex]

W = 2 x 9.8 x 26 = 509.6 Joule

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