A child rides a toboggan down a hill that descends at an angle of 15.5◦ to the horizontal. The hill is 48.1 m long. What is the vertical component of the child’s displacement? Answer in units of m.
Disp. = 48.1*sin15.5 =
To find the vertical component of the child's displacement, we need to determine the vertical distance traveled by the child.
The vertical component can be calculated using trigonometry. We can use the sine function to find the vertical distance.
Given:
Angle of descent (θ) = 15.5 degrees
Length of the hill (l) = 48.1 m
Step 1: Convert the angle from degree to radians.
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 15.5 * π / 180 ≈ 0.270
Step 2: Calculate the vertical component of the displacement.
Vertical component = length of the hill * sin(θ)
Vertical component = 48.1 * sin(0.270)
Using a calculator, we find that sin(0.270) ≈ 0.266
Vertical component ≈ 48.1 * (0.266) ≈ 12.793
Therefore, the vertical component of the child's displacement is approximately 12.793 m.