03_InstSolManual_PDF_Part17 - Motion in a Plane 3-17 3.56...

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3.56. Set Up: Use coordinates with the origin at the boy and with downward. The ball has and Solve: (a) The dog must travel horizontally the same distance the ball travels horizontally, so the dog must have speed (b) Use the vertical motion of the ball to find its time in the air. gives Then 3.57. Set Up: Use coordinates with the origin at the boy and with upward. The ball has and Solve: (a) The dog must travel horizontally the same distance the ball travels horizontally, so the dog must have speed (b) Use the vertical motion of the ball to find its time in the air. gives The quadratic formula gives The negative value is unphysical, so Then Reflect: The ball is in the air longer than when it is thrown horizontally (Problem 3.56), but it doesn’t travel as far horizontally. The dog doesn’t have to run as far or as fast as in Problem 3.56. 3.58. Set Up: Use coordinates with upward. Once the water leaves the cannon it is in free-fall and has and The water has and Solve: Use the vertical motion to find t that gives gives
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