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# A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are?

d1 = 4.04 m to the north, d2 = 2.08 m northeast, and d3 = 1.20 m at 30.0° west of south (see the figure below). Starting at the same initial point, an expert golfer could make the hole in what single displacement?

### 1 Answer

- kuiperbelt2003Lv 710 months agoFavorite Answer
Find the components of each stroke and sum. Let's call north and east positive; south and west negative.

The first stroke has a north component of 4.04 m; the second has the same component to the north and east, equal to 2.08 sin 45 (or equivalently, 2.08 cos 45) = 1.47m, and the third stroke has a south component of 1.2 cos 30 = 1.04m and a west component of 1.2 sin 30 = 0.6m

The total north/south motion is then 4.04 + 1.47 - 1.04 m = 4.47 m north

and a total east/west motion of 1.47 m - 0.6 m = 0.87 m east

the total magnitude of this is Sqrt[4.47^2 + 0.87^2] = 4.55 m,

and its direction is given by tan(theta) = 4.55/0.87 or an angle 79 degrees north of east

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