A superhero flies 285 m from the top of a
tall building at an angle of 20 ◦ below the
horizontal.
What is the horizontal component of the
superhero’s displacement? What is the vertical component of the superhero’s
displacement?
To find the horizontal and vertical components of the superhero's displacement, we can use trigonometric functions.
The horizontal component can be found using the cosine function, which relates the adjacent side to the hypotenuse of a right triangle. In this case, the adjacent side represents the horizontal displacement and the hypotenuse represents the total displacement.
To find the horizontal component, we can use the equation:
horizontal component = total displacement * cosine(angle)
Substituting the given values:
total displacement = 285 m
angle = 20°
horizontal component = 285 m * cos(20°)
Using a scientific calculator, we can calculate that the horizontal component of the superhero's displacement is approximately 270.025 m (rounded to three decimal places).
Next, let's find the vertical component of the superhero's displacement.
The vertical component can be found using the sine function, which relates the opposite side to the hypotenuse of a right triangle. In this case, the opposite side represents the vertical displacement and the hypotenuse represents the total displacement.
To find the vertical component, we can use the equation:
vertical component = total displacement * sine(angle)
Substituting the given values:
total displacement = 285 m
angle = 20°
vertical component = 285 m * sin(20°)
Using a scientific calculator, we can calculate that the vertical component of the superhero's displacement is approximately 96.474 m (rounded to three decimal places).
Therefore, the horizontal component of the superhero's displacement is approximately 270.025 m and the vertical component is approximately 96.474 m.