A child rides a toboggan down a hill that descends at an angle of 26.6 degrees to the horizontal. The hill is 13.1 meters long. What is the vertical component of the child's displacement? Answer in units of meters.
To find the vertical component of the child's displacement, we need to calculate the vertical distance the child moves.
First, let's define the given information:
- The angle of descent of the hill is 26.6 degrees.
- The length of the hill is 13.1 meters.
Now, we can use trigonometry to solve the problem.
The vertical component can be determined using the sine function, which relates the angle to the ratio between the opposite side and the hypotenuse of a right triangle.
In this case, the vertical distance is the opposite side and the length of the hill is the hypotenuse.
Using the sine function, we have:
sin(26.6°) = opposite / hypotenuse
Let's substitute the values:
sin(26.6°) = vertical distance / 13.1
To find the vertical component, we rearrange the equation:
vertical distance = sin(26.6°) * 13.1
Calculating the numerical result:
vertical distance ≈ 5.828 meters
Therefore, the vertical component of the child's displacement is approximately 5.828 meters.