A novice golfer on the green takes three
strokes to sink the ball. The successive dis-
placements are 5.9 m to the north, 10 m 45 �
north of east, and 5.9 m 26� west of south.
Starting at the same initial point, an expert
(lucky) golfer could make the hole in a single
displacement.
What is the magnitude of this single dis-
placement?
To find the magnitude of the single displacement made by the expert golfer, we need to add up the individual displacements made by the novice golfer.
Let's break down the novice golfer's displacements into their components:
1. The first displacement of 5.9 m to the north can be written as (0, 5.9). This means the displacement has no component along the east-west direction (x-axis) and only in the north-south direction (y-axis).
2. The second displacement of 10 m 45° north of east can be broken down into its x and y components. We'll use basic trigonometry to find these components:
- The x-component is given by 10 m * cos(45°) = 10 m * √(2)/2 = 5√2 m.
- The y-component is given by 10 m * sin(45°) = 10 m * √(2)/2 = 5√2 m.
Therefore, the second displacement can be written as (5√2, 5√2).
3. The third displacement of 5.9 m 26° west of south can also be broken down into its x and y components using trigonometry:
- The x-component is given by 5.9 m * cos(26°) = 5.9 m * cos(26°).
- The y-component is given by -5.9 m * sin(26°) = -5.9 m * sin(26°). (Note the negative sign as it points in the opposite direction of the y-axis.)
Therefore, the third displacement can be written as (5.9*cos(26°), -5.9*sin(26°)).
Now, let's add up these three displacements to find the net displacement:
Net displacement = (0 + 5√2 + 5.9*cos(26°), 5.9 + 5√2 - 5.9*sin(26°))
To find the magnitude of this net displacement, we use the Pythagorean theorem:
Magnitude of the net displacement = √(x-component^2 + y-component^2)
Let's calculate this to find the magnitude of the single displacement made by the expert golfer.