A superhero flies 310 m from the top of a
tall building at an angle of 15 ◦ below the
horizontal.
What is the horizontal component of the
superhero’s displacement? Draw the vectors
to scale on a graph to determine the answer.
Answer in units of m Your answer must be
within ± 5.0%
299.437
A superhero flies 310 m from the top of a
tall building at an angle of 15 ◦ below the
horizontal.
What is the horizontal component of the
superhero’s displacement?
To find the horizontal component of the superhero's displacement, we need to determine the length of the horizontal vector.
Given:
Vertical displacement (height) = 310 m
Angle below the horizontal = 15 degrees
To find the horizontal component, we can calculate it using trigonometry.
First, we need to determine the vertical displacement (y-component) using the height and the angle:
Vertical displacement = 310 m * sin(15 degrees) ≈ 79.84 m
Then, we can find the horizontal displacement (x-component) by subtracting the vertical displacement from the total displacement. Since the superhero flies straight downwards, the horizontal displacement is equal to the total displacement:
Horizontal displacement ≈ 310 m - 79.84 m = 230.16 m
Therefore, the horizontal component of the superhero's displacement is approximately 230.16 m.
To confirm our answer, we can draw a graph to scale. Let's assume that each unit on the graph represents 50 m. We should draw a vertical line of length 79.84 units and a horizontal line of length 230.16 units. By measuring the length of the horizontal line on the graph, we can verify that it is approximately equal to 230.16 m.
To determine the horizontal component of the superhero's displacement, we need to break down the given information into its horizontal and vertical components.
Given information:
- The superhero flies 310 m from the top of a tall building.
- The angle of descent is 15 degrees below the horizontal.
To find the horizontal component, we can start by determining the length of the side adjacent to the angle (the horizontal side). This can be done using the cosine function.
Cos θ = Adjacent / Hypotenuse
In this case, the adjacent side is the horizontal component of the superhero's displacement, and the hypotenuse is the total displacement of 310 m.
Cos 15° = Adjacent / 310
Rearranging the equation, we can solve for the horizontal component:
Adjacent = Cos 15° * 310
Calculating this on a calculator, we get:
Adjacent ≈ 292.755 m
Therefore, the horizontal component of the superhero's displacement is approximately 292.755 m.
To draw the vectors to scale on a graph, we can use a ruler or a graphing software. Start by drawing a horizontal line to represent the ground level. Then, draw a vertical line to represent the tall building. From the top of the building, draw a line at a 15-degree angle from the horizontal line. The length of this line should be 310 m. Now, from the endpoint of this line, draw a horizontal line back to the vertical line (ground level). The length of this horizontal line will be the horizontal component of the superhero's displacement, which is approximately 292.755 m.