A roller coaster goes 40-m along a section of track sloping 10 degrees below the horizontal, followed by a 13-m section sloping upward at 6 degrees, followed by an 26-m section of level track. Find the net displacement in m.

To find the net displacement, we need to calculate the vertical and horizontal components of displacement separately and then combine them.

First, let's calculate the vertical displacement. We'll consider upward as positive and downward as negative.

Vertical displacement = (vertical distance climbed) - (vertical distance descended)
= (13 m * sin(6 degrees)) - (40 m * sin(10 degrees))

Using a calculator, we can find the values of sin(6 degrees) and sin(10 degrees):

Vertical displacement = (13 * 0.1045) - (40 * 0.1736)
= 1.355 - 6.944
= -5.589 m (rounded to three decimal places)

Next, let's calculate the horizontal displacement:

Horizontal displacement = (13 m * cos(6 degrees)) + (40 m * cos(10 degrees)) + 26 m

Again, using a calculator, we can find the values of cos(6 degrees) and cos(10 degrees):

Horizontal displacement = (13 * 0.9945) + (40 * 0.9848) + 26
= 12.931 + 39.392 + 26
= 78.323 m (rounded to three decimal places)

Finally, we can find the net displacement by combining the vertical and horizontal displacements:

Net displacement = √((horizontal displacement)^2 + (vertical displacement)^2)

Net displacement = √((78.323)^2 + (-5.589)^2)
= √(6131.595 + 31.241)
= √(6162.836)
= 78.562 m (rounded to three decimal places)

Therefore, the net displacement is 78.562 meters.

To find the net displacement, we need to calculate the horizontal and vertical components of each section of the roller coaster track.

Let's break down each section and calculate their horizontal and vertical components:

1. The 40-m section sloping 10 degrees below the horizontal:
- Horizontal Component: 40 * cos(10°)
- Vertical Component: 40 * sin(10°)

2. The 13-m section sloping upward at 6 degrees:
- Horizontal Component: 13 * cos(6°)
- Vertical Component: -13 * sin(6°) (negative since it is sloping upward)

3. The 26-m section of level track:
- Horizontal Component: 26
- Vertical Component: 0 (since it is level)

Now, let's calculate each component:

1. Horizontal Component:
- 40 * cos(10°) ≈ 40 * 0.9848 ≈ 39.39 m

2. Vertical Component:
- 40 * sin(10°) ≈ 40 * 0.1736 ≈ 6.94 m
- -13 * sin(6°) ≈ -13 * 0.1045 ≈ -1.36 m (negative because it is sloping upward)

3. Horizontal Component:
- 26

Now, let's add up the horizontal and vertical components to find the net displacement:

Horizontal Displacement = 39.39 m + 13 m + 26 m = 78.39 m
Vertical Displacement = 6.94 m - 1.36 m + 0 m = 5.58 m

Therefore, the net displacement of the roller coaster is approximately 78.39 m to the right (positive direction) and 5.58 m upwards.