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# Homework 2_Graded - PROBLEM 11.110...

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PROBLEM 11.110 .~"""'~~~.'~~_~~0il'"",'~c"~"~"5;'~""'"> A golfer hits a ball with an initial velocity ofmagnitude Vo at an angle a with the. horizontal. Knowing that the ball must clear the tops oftwo trees andJand as close as possible to the flag, determine Vo and the distance d when the golfer uses (a) a six-iron with a = 31°, (b) a five-iron with a = 27°. SOLUTION The horizontal and vertical motions are x x (vocosa)t or Vo tcosa (1) . ) 1 2 1 2 Y = ( Vo sma t - - gt xtana --gt 2 2 2 2(xtana Y) or t = --'-------'--'- (2) g 2vo sina At the landing point C: 0, t Y c g sinacosa (3) And g (a) a=31° To clear tree A: XA 30m, YA = 12m (2 _ 2(30tan31° 12) = 1.22851 S2, From (2), fA = 1.1084 s A - 9.81 30 From (1), (vo) = 31.58m1s A 1.1084cos310 To clear tree B: XB = 100m, YB 14m 2(100tan31° -12) . 2 From (2), --'---------'- = 9.3957 s , tB 3.0652 s 9.81 From (1), (VO)B 100 38.06 mls 3.0652cos31° The larger value governs, Vo 38.06 mls Vo = 38.1 mls ~ x = (2)(38.06)2sin31°cos31° = 130.38m From (3), c 9.81 d = Xc -110 d = 20Am ~

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