A child rides a toboggan down a hill that

descends at an angle of 15.5

to the horizontal.
The hill is 13.8 m long.
What is the horizontal component of the
child’s displacement?
Answer in units of m
013 (part 2 of 2) 10.0 points
What is the vertical component of the child’s
displacement?

r(x)= 13.8•cos15.5◦

r(x)= 13.8•sin15.5◦

To find the horizontal component of the child's displacement, we need to find the part of the displacement that is in the horizontal direction.

Using trigonometry, we can find the horizontal component by using the formula:

horizontal component = displacement * cosine(angle)

In this case, the angle is given as 15.5 degrees and the displacement is given as 13.8 m.

So the horizontal component will be:
horizontal component = 13.8 m * cosine(15.5 degrees)

To find the vertical component of the child's displacement, we need to find the part of the displacement that is in the vertical direction.

Similarly, using trigonometry, we can find the vertical component by using the formula:

vertical component = displacement * sine(angle)

Again, the angle is given as 15.5 degrees and the displacement is given as 13.8 m.

So the vertical component will be:
vertical component = 13.8 m * sine(15.5 degrees)

Calculating these values using a calculator or a software, we find:

horizontal component = 13.8 m * 0.964966 = 13.32319 m (rounded to 5 decimal places)
vertical component = 13.8 m * 0.258819 = 3.570985 m (rounded to 6 decimal places)

Therefore, the horizontal component of the child's displacement is approximately 13.32319 m, and the vertical component of the child's displacement is approximately 3.570985 m.