A superhero flies 235 m from the top of a

tall building at an angle of 25 � 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%
What is the vertical component of the super-
hero’s displacement?
Answer in units of m Your answer must be
within ± 5.0%

To determine the horizontal and vertical components of the superhero's displacement, we can use trigonometry.

First, let's draw a diagram to visualize the problem. The superhero flies at an angle of 25 degrees below the horizontal. We can represent the superhero's displacement as a vector with a magnitude of 235 m and an angle of 25 degrees measured counterclockwise from the positive x-axis.

Now, let's calculate the horizontal component of the superhero's displacement. This can be found using the formula:

Horizontal component = Magnitude of displacement * cosine(angle)

So, the horizontal component of the superhero's displacement is:

Horizontal component = 235 m * cos(25 degrees)

To find the answer, we can evaluate this expression using a scientific calculator or a built-in calculator app on your computer or smartphone. Make sure your calculator is set to degree mode.

Horizontal component ≈ 235 m * 0.90631
Horizontal component ≈ 212.88 m

Therefore, the horizontal component of the superhero's displacement is approximately 212.88 m.

Next, let's calculate the vertical component of the superhero's displacement. This can be found using the formula:

Vertical component = Magnitude of displacement * sine(angle)

So, the vertical component of the superhero's displacement is:

Vertical component = 235 m * sin(25 degrees)

Again, we can evaluate this expression using a calculator in degree mode.

Vertical component ≈ 235 m * 0.42262
Vertical component ≈ 99.33 m

Therefore, the vertical component of the superhero's displacement is approximately 99.33 m.

To ensure the answer is within ±5.0% of the true value, we can use the following ranges:

Horizontal component: 212.88 m ± (5.0% of 212.88 m)
Vertical component: 99.33 m ± (5.0% of 99.33 m)

Just calculate 5.0% of each value and add/subtract it to/from the respective component to get the range.

Horizontal component range: 212.88 m ± (0.05 * 212.88 m)
Vertical component range: 99.33 m ± (0.05 * 99.33 m)

Simplifying,

Horizontal component range: 212.88 m ± 10.644 m
Vertical component range: 99.33 m ± 4.967 m

Therefore, the horizontal component of the superhero's displacement is between approximately 202.236 m and 223.524 m (212.88 m ± 10.644 m), and the vertical component is between approximately 94.363 m and 104.697 m (99.33 m ± 4.967 m).

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