Find the horizontal and vertical components of the d = 140 m displacement of a superhero who flies from the top of a tall building following the path shown in Fig. P3.18 where θ = 28.0°.
why do you assume we have any idea what Fig P3.18 shows?
To find the horizontal and vertical components of the displacement, we can use trigonometry. Let's break down the problem step by step:
Step 1: Understand the information given
- The displacement of the superhero is given as d = 140 m.
- The angle between the displacement and the horizontal direction is given as θ = 28.0°.
Step 2: Define the horizontal and vertical components
- The horizontal component of the displacement is the distance traveled in the horizontal direction.
- The vertical component of the displacement is the distance traveled in the vertical direction.
Step 3: Apply trigonometry to calculate the components
- The horizontal component (d_x) can be found using the formula: d_x = d * cos(θ).
- The vertical component (d_y) can be found using the formula: d_y = d * sin(θ).
Step 4: Calculate the components
- Substituting the given values into the formulas:
- d_x = 140 m * cos(28.0°)
- d_y = 140 m * sin(28.0°)
Step 5: Calculate the values
- Using a calculator, evaluate the cos(28.0°) and sin(28.0°) to find the values of d_x and d_y, respectively.
Step 6: Calculate the final answer
- The values of d_x and d_y will give you the horizontal and vertical components of the displacement of the superhero, respectively.
So, using the above steps, you can find the horizontal and vertical components of the displacement.