A child rides a toboggan down a hill that
descends at an angle of 20.7◦
to the horizontal.
The hill is 18.2 m long.
What is the horizontal component of the
child’s displacement?
Horizontal? 18.2 cosAngle
To find the horizontal component of the child's displacement, we need to find the horizontal distance traveled by the child down the hill.
Given:
Angle of descent (θ) = 20.7°
Length of the hill (h) = 18.2 m
To find the horizontal component, we can use the cosine function:
cos(θ) = adjacent / hypotenuse
In this case, the adjacent side is the horizontal component (x) and the hypotenuse is the length of the hill (h).
cos(20.7°) = x / 18.2 m
Rearranging the equation:
x = cos(20.7°) * 18.2 m
Using a calculator, we can evaluate the equation:
x ≈ 16.752 m
Therefore, the horizontal component of the child's displacement is approximately 16.752 m.
To find the horizontal component of the child's displacement, we first need to break down the displacement vector into its horizontal and vertical components.
Given:
Angle of the hill with respect to the horizontal (θ) = 20.7 degrees
Length of the hill (L) = 18.2 m
We can use trigonometry to calculate the horizontal component. The horizontal component of displacement can be found using the equation:
Horizontal component = Length of the hill * cos(θ)
Let's plug in the values to calculate the horizontal component:
Horizontal component = 18.2 m * cos(20.7 degrees)
To find the value of cos(20.7 degrees), you can use a scientific calculator or an online trigonometric calculator.
After evaluating the expression, the result will be the horizontal component of the child's displacement.