Answer :
To calculate how high the seagull was flying when it pooped, we can use the principles of physics related to free fall. Here's how the problem can be solved step-by-step:
1. Understand the Given Information:
- Impact velocity when the droppings hit: [tex]\(98.5 \, \text{m/s}\)[/tex]
- Acceleration due to gravity, [tex]\(g\)[/tex]: [tex]\(9.8 \, \text{m/s}^2\)[/tex]
2. Choose the Right Equation:
- We use the kinematic equation for free fall:
[tex]\[
v^2 = u^2 + 2gh
\][/tex]
Where:
- [tex]\(v\)[/tex] is the final velocity (impact velocity),
- [tex]\(u\)[/tex] is the initial velocity (0 m/s since the seagull wasn't moving vertically at the moment of pooping),
- [tex]\(g\)[/tex] is the acceleration due to gravity,
- [tex]\(h\)[/tex] is the height we are trying to find.
3. Simplify the Equation:
- Since the initial vertical velocity [tex]\(u\)[/tex] is 0, the equation simplifies to:
[tex]\[
v^2 = 2gh
\][/tex]
4. Solve for Height, [tex]\(h\)[/tex]:
- Rearrange the equation to solve for [tex]\(h\)[/tex]:
[tex]\[
h = \frac{v^2}{2g}
\][/tex]
5. Substitute the Values:
- Substitute [tex]\(v = 98.5 \, \text{m/s}\)[/tex] and [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex] into the equation:
[tex]\[
h = \frac{(98.5)^2}{2 \cdot 9.8}
\][/tex]
6. Calculate:
- After performing the calculation, we find:
[tex]\[
h \approx 495.01 \, \text{meters}
\][/tex]
Therefore, the seagull was flying approximately 495.01 meters high when it dropped the poop.
1. Understand the Given Information:
- Impact velocity when the droppings hit: [tex]\(98.5 \, \text{m/s}\)[/tex]
- Acceleration due to gravity, [tex]\(g\)[/tex]: [tex]\(9.8 \, \text{m/s}^2\)[/tex]
2. Choose the Right Equation:
- We use the kinematic equation for free fall:
[tex]\[
v^2 = u^2 + 2gh
\][/tex]
Where:
- [tex]\(v\)[/tex] is the final velocity (impact velocity),
- [tex]\(u\)[/tex] is the initial velocity (0 m/s since the seagull wasn't moving vertically at the moment of pooping),
- [tex]\(g\)[/tex] is the acceleration due to gravity,
- [tex]\(h\)[/tex] is the height we are trying to find.
3. Simplify the Equation:
- Since the initial vertical velocity [tex]\(u\)[/tex] is 0, the equation simplifies to:
[tex]\[
v^2 = 2gh
\][/tex]
4. Solve for Height, [tex]\(h\)[/tex]:
- Rearrange the equation to solve for [tex]\(h\)[/tex]:
[tex]\[
h = \frac{v^2}{2g}
\][/tex]
5. Substitute the Values:
- Substitute [tex]\(v = 98.5 \, \text{m/s}\)[/tex] and [tex]\(g = 9.8 \, \text{m/s}^2\)[/tex] into the equation:
[tex]\[
h = \frac{(98.5)^2}{2 \cdot 9.8}
\][/tex]
6. Calculate:
- After performing the calculation, we find:
[tex]\[
h \approx 495.01 \, \text{meters}
\][/tex]
Therefore, the seagull was flying approximately 495.01 meters high when it dropped the poop.
