A novice golfer on the green takes three

strokes to sink the ball. The successive displacements are 3.6 m to the north, 2.8 m 45◦ north of east, and 2.2 m 59◦ 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 displacement?

All angles are CCW from the +x-axis.

D = 3.6m[90o] + 2.8[45o] + 2.2[211o].

X = 3.6*Cos90 + 2.8*Cos45 + 2.2*cos211 =
0 + 1.98 - 1.89 = 0.09 m.

Y = 3.6*sin90 + 2.8*sin45 - 2.2*sin211 =
3.6 + 1.98 - 1.13 = 4.45 m.

D = Sqrt(X^2 + Y^2).

To find the magnitude of the single displacement, we can first break down the novice golfer's three successive displacements into their respective x and y components.

First Displacement: 3.6 m to the north
- The x component of this displacement is 0 m (no east/west component).
- The y component of this displacement is 3.6 m (north).

Second Displacement: 2.8 m 45° north of east
- To find the x and y components, we can use trigonometric functions. The angle is given as 45°, which means that the x and y components are equal.
- The x component of this displacement is 2.8 m * cos(45°) = 2.8 m * 0.707 ≈ 1.98 m (east).
- The y component of this displacement is 2.8 m * sin(45°) = 2.8 m * 0.707 ≈ 1.98 m (north).

Third Displacement: 2.2 m 59° west of south
- The x component of this displacement is 2.2 m * cos(59°) ≈ 2.2 m * -0.544 ≈ -1.197 m (west).
- The y component of this displacement is 2.2 m * sin(59°) ≈ 2.2 m * 0.841 ≈ 1.851 m (south).

Now we can add up the x and y components:
- The total x component is 0 m + 1.98 m - 1.197 m = 0.783 m (east).
- The total y component is 3.6 m + 1.98 m + 1.851 m = 7.431 m (north).

Now we can find the magnitude of the single displacement using the Pythagorean theorem:
Magnitude = √(x^2 + y^2)
Magnitude = √((0.783 m)^2 + (7.431 m)^2)
Magnitude = √(0.613 m^2 + 55.194 m^2)
Magnitude ≈ √55.807 m^2
Magnitude ≈ 7.47 m

Therefore, the magnitude of the single displacement made by the expert golfer is approximately 7.47 m.

To find the magnitude of the single displacement made by the expert golfer, we need to add up the three displacements made by the novice golfer.

Let's break down the displacements made by the novice golfer:

1. The first displacement is 3.6 m to the north. This displacement is purely in the north direction, so we can represent it as (0, 3.6) in vector notation.

2. The second displacement is 2.8 m 45◦ north of east. To break this down into its x and y components, we can use trigonometry:

- The angle 45◦ north of east can be converted to 45◦ clockwise from the positive x-axis.
- The x-component can be found by multiplying the magnitude (2.8 m) by the cosine of 45◦.
- The y-component can be found by multiplying the magnitude (2.8 m) by the sine of 45◦.

Thus, the second displacement can be represented as (2.8 * cos(45◦), 2.8 * sin(45◦)) in vector notation.

3. The third displacement is 2.2 m 59◦ west of south. To break this down into its x and y components, we can use trigonometry:

- The angle 59◦ west of south can be converted to 59◦ clockwise from the positive y-axis.
- The x-component can be found by multiplying the magnitude (2.2 m) by the sine of 59◦ (opposite of sine when measuring from the positive y-axis).
- The y-component can be found by multiplying the magnitude (2.2 m) by the cosine of 59◦ (adjacent of sine when measuring from the positive y-axis).

Thus, the third displacement can be represented as (2.2 * -sin(59◦), 2.2 * cos(59◦)) in vector notation.

Now, we can add up the three displacements of the novice golfer:

(0, 3.6) + (2.8 * cos(45◦), 2.8 * sin(45◦)) + (2.2 * -sin(59◦), 2.2 * cos(59◦))

Calculating this sum, we get the resultant displacement made by the novice golfer.

To find the magnitude of this resultant displacement, we can use the Pythagorean theorem:

Magnitude = sqrt((sum_of_squares_of_x_components) + (sum_of_squares_of_y_components))

Plug in the values obtained from the sum of the three displacements into this equation to find the magnitude of the single displacement made by the expert golfer.