On the surface of the earth, the gravitational field (with z as vertical coordinate measured in meters) is F = 〈 0 , 0 , − g 〉 . (a) Find the potential function for F. (b) Beginning at rest, a ball of mass m = 2 k g moves under the influence of gravity (without friction) along a path from P = ( 3 , 2 , 400 ) to Q = ( − 21 , 40 , 50 ) . Find the balls velocity when it reaches Q.

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Chapter 17.3, Problem 29E

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To determine:

On the surface of the earth, the gravitational field (with z as vertical coordinate measured in meters) is $F = 〈 0, 0, - g 〉$ .

(a) Find the potential function for F.

(b) Beginning at rest, a ball of mass $m = 2 k g$ moves under the influence of gravity (without friction) along a path from $P = (3, 2, 400)$ to $Q = (- 21, 40, 50)$ . Find the balls velocity when it reaches Q.

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