A superhero flies 185 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%
To find the horizontal component of the superhero's displacement, we need to determine the horizontal distance traveled.
Given:
Vertical distance (height) = 185 m
Angle below horizontal = 15°
We can use trigonometry to solve this problem. The vertical distance traveled can be represented by the equation:
Vertical distance = Horizontal distance * tan(angle)
Rearranging the equation, we have:
Horizontal distance = Vertical distance / tan(angle)
Now, substituting the given values:
Horizontal distance = 185 m / tan(15°) ≈ 642.45 m
Therefore, the horizontal component of the superhero's displacement is approximately 642.45 m.
To visualize this, we can draw a graph. Choose a scale that represents 1 cm equal to a certain distance, such as 100 m. On the horizontal axis, draw a distance of 642.45 m. On the vertical axis, draw 185 m. Connect the two points and label the resultant line as the superhero's displacement vector. Note that the horizontal component of the displacement will be parallel to the x-axis.
Remember that when drawing to scale, the accuracy may be affected. Therefore, your answer must be within ± 5.0% of the exact value, considering the limitations of the scale on your graph.