Here is my question: A novice golfer on the green takes three strokes to sink th

Question

Here is my question:

A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are d1 = 3.94 m to the north, d2 = 1.92 m northeast, and d3 = 1.16 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?

I found the magnitude to be 4.38 m which is the correct answer. I calculated the direction to be 25.9 degrees north of east, but that's wrong. If you could help me find the direction that would be great.

Explanation / Answer

here ,

let us assume as east as positive x - direction

north as positive y - direction

d1 = 3.94 j m

d2 = 1.92 * (cos(45) i + j * sin(45))

d2 = 1.36 i + 1.36 j

d3 = 1.16 * (-sin(30)i - j * cos(30) )

d3 = -0.58 i - 1 j m

Now, for the single displacement

d = d1 + d2 + d3

d = 3.94 j m + 1.36 i + 1.36 j -0.58 i - 1 j m

d = 0.78 i + 4.3 j

magnitude of displacement = sqrt(0.78^2 + 4.3^2)

magnitude of displacement = 4.38 m

the magnitude of displacement is 4.38 m

direction = arctan(4.3/0.78)

direction = 79.7 degree

the direction of displacement is 79.7 degree north of east

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