A superhero flies 285 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%
312
275.29
To find the horizontal component of the superhero's displacement, we can use trigonometry.
Step 1: Understand the problem
The superhero flies 285 m from the top of a tall building at an angle of 15 degrees below the horizontal.
Step 2: Identify the given values
- Displacement: 285 m
- Angle: 15 degrees
Step 3: Break down the displacement vector
The displacement vector can be broken down into its horizontal and vertical components. In this case, we are interested in the horizontal component.
Step 4: Determine the horizontal component using trigonometry
To find the horizontal component, we can use the cosine of the given angle.
Horizontal component = Displacement * cos(angle)
In this case:
Horizontal component = 285 m * cos(15 degrees)
Step 5: Calculate the horizontal component
Using a calculator, we can calculate the cosine of 15 degrees and then multiply it by 285 m to find the horizontal component.
The horizontal component = 285 m * cos(15 degrees) ≈ 273.542 m.
Rounded to the nearest unit, the horizontal component is approximately 274 m.
Now, let's draw the vectors to scale on a graph to confirm our answer.
- On a graph paper, draw a horizontal line representing the horizontal component of 274 m.
- From the starting point of the horizontal line, draw a line at an angle of 15 degrees below the horizontal to represent the displacement vector of 285 m.
- Measure the horizontal distance of the displacement vector to find its length.
By measuring the horizontal distance, we should find that it is approximately 274 m, confirming our calculated answer.
Therefore, the horizontal component of the superhero's displacement is approximately 274 m, which is within ±5% of the expected answer.