A superhero flies 235 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?
Your answer must be within ± 5.0%
I also need to know how to get the vertical component of his displacement.
227
To find the horizontal component of the superhero's displacement, we can use trigonometry.
The given angle of 15° below the horizontal is the angle between the direction of motion and the horizontal axis.
The horizontal component of the displacement can be found using the formula:
Horizontal displacement = Displacement * cos(angle)
Here, the displacement is given as 235 m.
So, the horizontal component can be calculated as:
Horizontal displacement = 235 m * cos(15°)
Let's calculate it.
Horizontal displacement = 235 m * cos(15°)
Horizontal displacement ≈ 235 m * 0.9659
Horizontal displacement ≈ 226.763 m
Therefore, the horizontal component of the superhero's displacement is approximately 226.763 m.
To find the horizontal component of the superhero's displacement, we can use trigonometry.
First, let's represent the given information:
- The distance traveled by the superhero is 235 m
- The angle of 15 degrees below the horizontal
To find the horizontal component, we need to find the cosine of the given angle. The cosine of an angle represents the ratio of the adjacent side to the hypotenuse in a right triangle.
Cosine of an angle (θ) = Adjacent side / Hypotenuse
In this case, the adjacent side represents the horizontal component of the displacement, and the hypotenuse represents the total displacement traveled by the superhero.
So, the equation becomes:
Cos(15 degrees) = Horizontal Component / 235 m
Now we can rearrange the equation to find the horizontal component:
Horizontal Component = Cos(15 degrees) * 235 m
Using a calculator, we can find the value of the cosine of 15 degrees, which is approximately 0.9659.
So, the horizontal component of the superhero's displacement is:
Horizontal Component = 0.9659 * 235 m
Evaluating this equation, we get:
Horizontal Component ≈ 227.6125 m
Therefore, the horizontal component of the superhero's displacement is approximately 227.6125 m.
Considering the given tolerance of ± 5.0%, the acceptable range of values for the horizontal component would be within:
227.6125 m ± 5.0%
This means the acceptable range would be:
227.6125 m ± (0.05 * 227.6125 m)
Calculating this, we get:
Acceptable range = 227.6125 m ± 11.380625 m
So, the acceptable range for the horizontal component of the superhero's displacement is approximately:
(227.6125 m - 11.380625 m) to (227.6125 m + 11.380625 m)
which is:
~ 216.231875 m to ~ 238.993125 m