To crack open a 300 g clam, a herring gull needs to provide 25 J of gravitational potential energy.

Calculate how high the bird needs to fly to crack the clam's shell.

Hint: Make sure you use the standard units in your calculation.

To solve this problem, we need to calculate the height to which a herring gull must fly to provide enough gravitational potential energy (GPE) to crack open a clam. The gravitational potential energy is given by the formula:

\[
\text{GPE} = mgh
\]

where:
- \( \text{GPE} \) is the gravitational potential energy in joules (J),
- \( m \) is the mass in kilograms (kg),
- \( g \) is the acceleration due to gravity (in meters per second squared, m/s²),
- \( h \) is the height in meters (m).

### Given:
- The mass of the clam, \( m = 300 \) grams (g).
- Gravitational potential energy needed, \( \text{GPE} = 25 \) joules (J).
- Acceleration due to gravity, \( g = 9.8 \) m/s².

### Step-by-Step Solution:

1. **Convert the mass of the clam from grams to kilograms:**

\[
m = 300 \, \text{g} = 300 \times 10^{-3} \, \text{kg} = 0.3 \, \text{kg}
\]

2. **Rearrange the gravitational potential energy formula to solve for height \( h \):**

\[
h = \frac{\text{GPE}}{mg}
\]

3. **Plug in the values:**

\[
h = \frac{25 \, \text{J}}{0.3 \, \text{kg} \times 9.8 \, \text{m/s}^2}
\]

4. **Calculate the height:**

\[
h = \frac{25}{0.3 \times 9.8}
\]

\[
h = \frac{25}{2.94}
\]

\[
h \approx 8.5 \, \text{m}
\]

### Conclusion:

The herring gull needs to fly to a height of approximately **8.5 meters** to crack the clam's shell.

Would you like more details on any part of this calculation or have any questions?  

Here are some related questions you might find interesting:

1. How would the required height change if the mass of the clam were doubled?
2. What would happen if the gravitational acceleration were different, such as on the Moon?
3. How much energy would be required if the clam’s mass were 400 grams?
4. If the bird flies at a constant speed up to 8.5 meters, how long would it take assuming a certain speed?
5. What is the energy conversion process from the bird’s height to the cracking of the clam?

**Tip:** When working with units in physics, always ensure they are consistent to avoid calculation errors.

Learn how to calculate the height a herring gull needs to fly to crack a clam's shell using gravitational potential energy. Detailed step-by-step solution with units and conversion. Suitable for physics students in Grades 9-12.

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