A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are d1 = 3.95 m to the north, d2 = 1.91 m northeast, and d3 = 1.16 m at 30.0° west of south (see the figure). Starting at the same initial point, an expert golfer could make the hole in what single displacement?

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47 To find the single displacement for the expert golfer to make the hole, we need to combine the individual displacements (d1, d2, and d3) into a single resultant displacement.

First, let's represent the displacements using vectors:

d1 = 3.95 m north (represented as a vector: d1 = 3.95 m north)
d2 = 1.91 m northeast (represented as a vector: d2 = 1.91 m at 45° north of east)
d3 = 1.16 m at 30.0° west of south (represented as a vector: d3 = -1.16 m at 30.0° south of west)

Now, let's calculate the x and y components of each displacement:

For d1:
- x component: 0 m (since it is north-south displacement)
- y component: 3.95 m

For d2:
- x component: cos(45°) * 1.91 m
- y component: sin(45°) * 1.91 m

For d3:
- x component: cos(30.0°) * -1.16 m
- y component: sin(30.0°) * -1.16 m

Now, add up the x and y components:

x component: 0 + cos(45°) * 1.91 m + cos(30.0°) * -1.16 m
y component: 3.95 m + sin(45°) * 1.91 m + sin(30.0°) * -1.16 m

Finally, calculate the magnitude and angle of the resultant displacement:

magnitude: sqrt((x component)^2 + (y component)^2)
angle: tan^(-1)((y component) / (x component))

This will give us the magnitude and direction of the single displacement the expert golfer needs to make the hole.