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

Update:

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?

Relevance

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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