A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is the skier's displacement from his starting point?

To find the skier's displacement, we can use vector addition.

The skier's horizontal displacement is 100.0 m.

Next, we need to find the vertical displacement, which is the distance traveled uphill. We can calculate it using trigonometry.

Given:
Distance uphill = 35.0 m
Angle above the horizontal = 35.0º

The vertical displacement is calculated as follows:
Vertical displacement = Distance uphill × sin(angle)
Vertical displacement = 35.0 m × sin(35.0º)

Using a calculator, we can find the sine of 35.0º is approximately 0.5736.

Vertical displacement = 35.0 m × 0.5736
Vertical displacement ≈ 20.071 m (rounded to three decimal places)

Finally, we can find the skier's displacement from his starting point using Pythagoras' theorem:

Displacement = √(Horizontal displacement² + Vertical displacement²)
Displacement = √(100.0 m² + 20.071 m²)
Displacement = √(10000 m² + 402.861441 m²)
Displacement ≈ √(10402.861441 m²)
Displacement ≈ 102.003 m (rounded to three decimal places)

Therefore, the skier's displacement from his starting point is approximately 102.003 meters.

To find the skier's displacement from his starting point, we need to calculate the vector sum of his horizontal displacement and his uphill displacement.

First, let's break down the horizontal and uphill displacements into their components. For the horizontal displacement of 100.0 m, there is no vertical component as the skier moves only along the horizontal axis. Therefore, the horizontal component is 100.0 m, and the vertical component is 0 m.

For the uphill displacement of 35.0 m at an angle of 35.0º above the horizontal, we need to find its horizontal and vertical components. The horizontal component can be found using the formula:

horizontal component = displacement * cos(angle)

horizontal component = 35.0 m * cos(35.0º)

Using a calculator, we find that the horizontal component is approximately 28.80 m.

Similarly, the vertical component can be found using the formula:

vertical component = displacement * sin(angle)

vertical component = 35.0 m * sin(35.0º)

Using a calculator, we find that the vertical component is approximately 19.89 m.

Now, let's calculate the skier's displacement by adding the horizontal and vertical components.

Horizontal displacement = 100.0 m + 28.80 m ≈ 128.80 m
Vertical displacement = 0 m + 19.89 m ≈ 19.89 m

To find the displacement from the starting point, we can use the Pythagorean theorem:

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

displacement = √(128.80 m^2 + 19.89 m^2)

Using a calculator, we find that the skier's displacement from his starting point is approximately 130.87 m.

horizontal

x = 100 + 35 cos 35

vertical
y = 35 sin 35

or
sqrt(x^2+y^2) at tan^-1(y/x) above x axis

A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is the skier's displacement from his starting point?