Question

It's been a great day of new, frictionless snow. Julie starts at the top of the 60? slope shown in the figure (Figure 1). At the bottom, a circular arc carries her through a 90? turn, and she then launches off a3.0-m-high ramp.

It's been a great day of new, frictionless snow.

How far horizontally is her touchdown point from the end of the ramp?

Answer 1

To find the horizontal distance of Julie's touchdown point from the end of the ramp, we can use trigonometry to calculate the horizontal distances traveled on the slope and during the circular arc.

Step-by-step explanation:

To find the horizontal distance of Julie's touchdown point from the end of the ramp, we need to calculate the distance traveled horizontally during her motion. From the information provided, we know that Julie starts at the top of a 60° slope, goes through a 90° turn, and then launches off a 3.0m-high ramp. We can use trigonometry to solve this problem.

First, let's find the horizontal distance traveled on the slope. Using the trigonometric function cosine, we can calculate the horizontal component of the displacement as follows:

horizontal distance = 2.5m * cos(60°)

Next, let's calculate the horizontal distance traveled during the circular arc. Considering the radius of the circular arc is the same as the height of the ramp, we can use the formula for the circumference of a circle to find the distance:

horizontal distance = 2π * 3.0m / 4

Finally, we can add the two horizontal distances calculated above to find the total horizontal distance Julie travels from the end of the ramp.